Publications
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Optimal mean-time path planning for unmanned underwater vehicles: a Hamilton-Jacobi approach
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Non-intrusive global-local method for poroelasticity problems with localized pressure effects.
BibTeX
@misc{KunwarLeeYi2025Submitted, title = {Non-intrusive global-local method for poroelasticity problems with localized pressure effects}, author = {Kunwar, Hemanta and Lee, Sanghyun and Yi, Son-Young}, year = {2025}, note = {Submitted} } -
Stability analysis of the fixed stress schemes in poroelastodynamics
BibTeX
@misc{KunwarLeeYi2025Submitted, title = {Non-intrusive global-local method for poroelasticity problems with localized pressure effects}, author = {Kunwar, Hemanta and Lee, Sanghyun and Yi, Son-Young}, year = {2025}, note = {Submitted} } -
Ensemble Score Filter for Data Assimilation of Two-Phase Flow Models in Porous MediaIn revision, Journal of Computational Physics
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Convergence and Numerical Simulations of the Continuous Data Assimilation for Biot's Poroelasticity System
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A Machine Learning and Finite Element Framework for Inverse Elliptic PDEs via Dirichlet-to-Neumann Mapping
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A Posteriori Error Estimation for Parabolic Equations with Enriched Galerkin Finite Element Methods
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Bound-preserving and entropy stable enriched Galerkin methods for nonlinear hyperbolic equationsIn revision, Journal of Computational Physics
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A thermo-flow-mechanics-fracture model employing a high-accuracy phase-field interface approachInternational Journal for Numerical Methods in Engineering, 126: e7646 (2025).
BibTeX
@article{LeeWahlWick_2025, author = {Lee, Sanghyun and von Wahl, Henry and Wick, Thomas}, title = {A Thermo-Flow-Mechanics-Fracture Model Coupling a Phase-Field Interface Approach and Thermo-Fluid-Structure Interaction}, journal = {International Journal for Numerical Methods in Engineering}, volume = {126}, number = {1}, pages = {e7646}, keywords = {fracture, phase-field, sharp interface, smeared interface, thermo-fluid-structure interaction, thermo-hydro-mechanics}, doi = {https://doi.org/10.1002/nme.7646}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7646}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.7646}, abstract = {ABSTRACT This work proposes a novel approach for coupling non-isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid-filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface-capturing phase-field fracture method and interface-tracking thermo-fluid-structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase-field approach to represent fractures and reconstruct the geometry to frame a thermo-fluid-structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase-field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid-filled fracture with the phase-field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase-field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures.}, year = {2025} } -
A phase-field diffraction model for thermo-hydro-mechanical propagating fracturesInternational Journal of Heat and Mass Transfer, Vol. 239, 126487 (April 2025).
BibTeX
@article{LeeWheelerWick_2025, title = {A phase-field diffraction model for thermo-hydro-mechanical propagating fractures}, journal = {International Journal of Heat and Mass Transfer}, volume = {239}, pages = {126487}, year = {2025}, issn = {0017-9310}, doi = {https://doi.org/10.1016/j.ijheatmasstransfer.2024.126487}, url = {https://www.sciencedirect.com/science/article/pii/S0017931024013152}, author = {Sanghyun Lee and Mary F. Wheeler and Thomas Wick}, keywords = {Thermo-poroelasticity, Phase-field fracture, Fixed-stress, Diffraction systems, Physics-based discretization, IPACS}, abstract = {This paper introduces a novel diffraction based thermo-hydraulicâmechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variablesâdisplacements, phase-field, pressure, and temperatureâeach governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservationâcrucial aspects for THM problems and realistic behavior. Moreover, the use of a predictorâcorrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. These new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.} } -
Optimal Control for Darcy's flow in a heterogeneous porous mediaApplied Numerical Mathematics, Volume 207, January 2025, Pages 303-322.
BibTeX
@article{JeongLee_2023, title = {Optimal control for Darcy's equation in a heterogeneous porous media}, journal = {Applied Numerical Mathematics}, volume = {207}, pages = {303-322}, year = {2025}, issn = {0168-9274}, doi = {https://doi.org/10.1016/j.apnum.2024.08.027}, url = {https://www.sciencedirect.com/science/article/pii/S0168927424002319}, author = {SeongHee Jeong and Sanghyun Lee}, keywords = {Optimal control, Darcy's flow, Heterogeneity, interior penalty}, abstract = {In this paper, we investigate optimal control problems in heterogeneous porous media. The optimal control problem is governed by the Darcy's flow equation; where the pressure is the state variable and the source/sink is the control variable. Then we introduce the reduced optimal control problem which contains only the state variable by replacing the control variable with a dependent quantity of the state variable based on the Darcy's equation. Here we employ C0 interior penalty finite element methods for the spatial discretization to solve the reduced optimal control problem resulting in a fourth-order variational inequality. We use P2 Lagrange finite elements for C0 interior penalty methods, which require fewer degrees of freedom than C1 finite element methods. We provide a priori error estimates and stability analyses by considering a heterogeneous permeability coefficient. Several numerical examples validate the given theories and illustrate the capabilities of the proposed algorithm.} } -
Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity modelNumerische Mathematik, 156: 949-978 (2024).
BibTeX
@article{YiLee2024physics, title={Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model}, author={Yi, Son-Young and Lee, Sanghyun}, journal={Numerische Mathematik}, volume={156}, number={3}, pages={949--978}, year={2024}, publisher={Springer} } -
A novel technique for minimizing energy functional using neural networksEngineering Applications of Artificial Intelligence, 133 (Part D), July 2024, 108313.
BibTeX
@article{PoudelLee_2024, title = {A novel technique for minimizing energy functional using neural networks}, journal = {Engineering Applications of Artificial Intelligence}, volume = {133}, pages = {108313}, year = {2024}, issn = {0952-1976}, doi = {https://doi.org/10.1016/j.engappai.2024.108313}, url = {https://www.sciencedirect.com/science/article/pii/S0952197624004718}, author = {Sanjeeb Poudel and Xiaoqiang Wang and Sanghyun Lee}, keywords = {Neural networks, Energy minimization, Heat energy, Lyapunov energy, Elastic bending energy}, abstract = {An energy functional describes the equilibrium state of a system. In this work, we present a novel technique, Functional Optimization using Neural Networks (FONN), for minimizing the systemâs energy. FONN utilizes neural networks to process information at discrete grid points, considering their interactions with neighboring grid points, to update the state of the system. The training process involves formulating a loss function based on the systemâs energy, and with the help of multiple fine-tuning steps, the method employs a progressive energy reduction technique that decreases the energy in multiple steps. FONNâs effectiveness is demonstrated across various problems, including the minimization of the heat and Lyapunov energy. Moreover, the paper explores the minimization of the elastic bending energy with an area constraint.} } -
Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticityResults in Applied Mathematics, Volume 21 (Feb 2024), 100430.
BibTeX
@article{BALLARIN2024100430, title = {Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity}, journal = {Results in Applied Mathematics}, volume = {21}, pages = {100430}, year = {2024}, issn = {2590-0374}, doi = {https://doi.org/10.1016/j.rinam.2023.100430}, url = {https://www.sciencedirect.com/science/article/pii/S2590037423000766}, author = {Francesco Ballarin and Sanghyun Lee and Son-Young Yi}, keywords = {Linear thermo-poroelasticity, Iterative, Fixed-stress, Reduced order modeling, Proper orthogonal decomposition}, abstract = {This paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biotâs poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess.} } -
On the training and generalization of deep operator networksSIAM Journal on Scientific Computing, Vol. 46, Iss. 4 (2024).
BibTeX
@article{LeeShin_2024, author = {Lee, Sanghyun and Shin, Yeonjong}, title = {On the Training and Generalization of Deep Operator Networks}, journal = {SIAM Journal on Scientific Computing}, volume = {46}, number = {4}, pages = {C273-C296}, year = {2024}, doi = {10.1137/23M1598751}, URL = {https://doi.org/10.1137/23M1598751}, abstract = { Abstract. We present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the GramâSchmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media. } } -
A thermal-hydraulic-mechanical-chemical coupling model for acid fracture propagation based on a phase-field methodRock Mechanics and Rock Engineering, 57: 4583-4605 (2024).
BibTeX
@article{dai_thmc_2024, title={A thermal--hydraulic--mechanical--chemical coupling model for acid fracture propagation based on a phase-field method}, author={Dai, Yifan and Hou, Bing and Lee, Sanghyun and Wick, Thomas}, journal={Rock Mechanics and Rock Engineering}, volume={57}, number={7}, pages={4583--4605}, year={2024}, publisher={Springer Nature BV} } -
Locking-free and locally-conservative enriched Galerkin method for poroelasticityJournal of Scientific Computing, 94:26 (2023).
BibTeX
@article{lee2023locking, title={Locking-free and locally-conservative enriched Galerkin method for poroelasticity}, author={Lee, Sanghyun and Yi, Son-Young}, journal={Journal of Scientific Computing}, volume={94}, number={1}, pages={26}, year={2023}, publisher={Springer} } -
Enhancing high-fidelity nonlinear solver with reduced order modelScientific Reports, 12(1):1-15 (2022).
BibTeX
@article{kadeethum2022enhancing, title={Enhancing high-fidelity nonlinear solver with reduced order model}, author={Kadeethum, Teeratorn and O’malley, Daniel and Ballarin, Francesco and Ang, Ida and Fuhg, Jan N and Bouklas, Nikolaos and Silva, Vinicius LS and Salinas, Pablo and Heaney, Claire E and Pain, Christopher C and others}, journal={Scientific reports}, volume={12}, number={1}, pages={20229}, year={2022}, publisher={Nature Publishing Group UK London} } -
An Enriched Galerkin method for the Stokes equationsComputers & Mathematics with Applications, 120 (15 Aug 2022): 115-131.
BibTeX
@article{YI2022115, title = {An enriched Galerkin method for the Stokes equations}, journal = {Computers & Mathematics with Applications}, volume = {120}, pages = {115-131}, year = {2022}, issn = {0898-1221}, doi = {https://doi.org/10.1016/j.camwa.2022.06.018}, url = {https://www.sciencedirect.com/science/article/pii/S0898122122002632}, author = {Son-Young Yi and Xiaozhe Hu and Sanghyun Lee and James H. Adler}, keywords = {Enriched Galerkin, Stokes, Finite element method, Inf-sup}, abstract = {We present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressure. The proposed EG method augments the conforming piecewise linear space for velocity by adding an additional degree of freedom which corresponds to one discontinuous linear basis function per element. Thus, the total number of degrees of freedom is significantly reduced in comparison with standard conforming, non-conforming, and discontinuous Galerkin schemes for the Stokes equation. We show the well-posedness of the new EG approach and prove that the scheme converges optimally. For the solution of the resulting large-scale indefinite linear systems we propose robust block preconditioners, yielding scalable results independent of the discretization and physical parameters. Numerical results confirm the convergence rates of the discretization and also the robustness of the linear solvers for a variety of test problems.} } -
Numerical simulation of pores connection by acid fracturing based on phase field methodActa Petrolei Sinica, 43(6), 849-859 (2022).
BibTeX
@article{hou2022numerical, title={Numerical simulation of pores connection by acid fracturing based on phase field method}, author={Hou, Bing and Dai Yifan, Fan Meng and Zhang, Kunpeng and Wick, Thomas and Lee, Sanghyun}, journal={Acta Petrolei Sinica}, volume={43}, number={6}, pages={849}, year={2022} } -
Physics-Informed neural networks for solving coupled flow and transport systemAAAI 2021.
BibTeX
@inproceedings{lee2021physics, title={Physics-informed Neural Networks for Solving Coupled Flow and Transport System.}, author={Lee, Sanghyun and Kadeethum, Teeratorn}, booktitle={AAAI Spring Symposium: MLPS}, pages={436--450}, year={2021} } -
Locking-free enriched Galerkin method for linear elasticitySIAM Journal on Numerical Analysis, 60(1):52-75 (2022).
BibTeX
@article{doi:10.1137/21M1391353, author = {Yi, Son-Young and Lee, Sanghyun and Zikatanov, Ludmil}, title = {Locking-Free Enriched Galerkin Method for Linear Elasticity}, journal = {SIAM Journal on Numerical Analysis}, volume = {60}, number = {1}, pages = {52-75}, year = {2022}, doi = {10.1137/21M1391353}, abstract = { We propose a new locking-free enriched Galerkin method for solving the linear elasticity problem. The method is based on the discontinuous Galerkin formulation, but its approximation space is a continuous piecewise linear vector-valued function space enriched by some discontinuous piecewise linear functions. An a priori error estimate of optimal order in the energy norm is proved and shown to be independent of a Lamé parameter \$\lambda\$, hence the proposed method is free of volumetric locking when modeling incompressible materials. Moreover, a uniform preconditioner with respect to the mesh size is established in the operator preconditioning framework. We provide several numerical examples to confirm the accuracy and the robustness of the new method and demonstrate a good performance of the preconditioner. } } -
A Locally Conservative Finite Element Framework for Coupled Hydro-Mechanical-Chemical Processes in Heterogeneous Porous MediaComputers & Geosciences, 152 (2021) 104774.
BibTeX
@article{KADEETHUM2021104774, title = {A locally conservative mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media}, journal = {Computers & Geosciences}, volume = {152}, pages = {104774}, year = {2021}, issn = {0098-3004}, doi = {https://doi.org/10.1016/j.cageo.2021.104774}, url = {https://www.sciencedirect.com/science/article/pii/S0098300421000790}, author = {T. Kadeethum and S. Lee and F. Ballarin and J. Choo and H.M. Nick}, keywords = {Hydro-mechanical–chemical coupling, Poroelasticity, Reactive flow, Mixed finite element method, Enriched Galerkin method, Local conservation}, abstract = {This paper presents a mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin method for reactive flow, and (2) a three-field mixed finite element method for coupled fluid flow and solid deformation. This combination ensures local mass conservation, which is critical to flow and transport in heterogeneous porous media, with a relatively affordable computational cost. A particular class of the framework is constructed for calcite precipitation/dissolution reactions, incorporating their nonlinear effects on the fluid viscosity and solid deformation. Linearization schemes and algorithms for solving the nonlinear algebraic system are also presented. Through numerical examples of various complexity, we demonstrate that the proposed framework is a robust and efficient computational method for simulation of reactive flow and transport in deformable porous media, even when the material properties are strongly heterogeneous and anisotropic.} } -
Finite element simulation of quasi-static tensile fracture in nonlinear strain-limiting solids with the phase-field approachJournal of Computational and Applied Mathematics, 399 (2022) 113715.
BibTeX
@article{LEE2022113715, title = {Finite element simulation of quasi-static tensile fracture in nonlinear strain-limiting solids with the phase-field approach}, journal = {Journal of Computational and Applied Mathematics}, volume = {399}, pages = {113715}, year = {2022}, issn = {0377-0427}, doi = {https://doi.org/10.1016/j.cam.2021.113715}, url = {https://www.sciencedirect.com/science/article/pii/S037704272100337X}, author = {Sanghyun Lee and Hyun Chul Yoon and S.M. Mallikarjunaiah}, keywords = {Strain-limiting model, Nonlinear elasticity, LEFM, Fracture propagation, Phase-field, Finite element method}, abstract = {We investigate a quasi-static tensile fracture in nonlinear strain-limiting solids by coupling with the phase-field approach. A classical model for the growth of fractures in an elastic material is formulated in the framework of linear elasticity for deformation systems. This linear elastic fracture mechanics (LEFM) model is derived based on the assumption of small strain. However, the boundary value problem formulated within the LEFM and under traction-free boundary conditions predicts large singular crack-tip strains. Fundamentally, this result is directly in contradiction with the underlying assumption of small strain. In this work, we study a theoretical framework of nonlinear strain-limiting models, which are algebraic nonlinear relations between stress and strain. These models are consistent with the basic assumption of small strain. The advantage of such framework over the LEFM is that the strain remains bounded even if the crack-tip stress tends to the infinity. Then, employing the phase-field approach, the distinct predictions for tensile crack growth can be governed by the model. Several numerical examples to evaluate the efficacy and the performance of the model and numerical algorithms structured on finite element method are presented. Detailed comparisons of the strain, fracture energy with corresponding discrete propagation speed between the nonlinear strain-limiting model and the LEFM for the quasi-static tensile fracture are discussed.} } -
Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot's System by Employing Machine LearningInternational Journal of Numerical Analysis and Modeling, 21 (2024), 764-792.
BibTeX
@article{lee2024choice, title={CHOICE OF INTERIOR PENALTY COEFFICIENT FOR INTERIOR PENALTY DISCONTINUOUS GALERKIN METHOD FOR BIOT’S SYSTEM BY EMPLOYING MACHINE LEARNING.}, author={Lee, Sanghyun and Kadeethum, Teeratorn and Nick, Hamidreza M}, journal={International Journal of Numerical Analysis \& Modeling}, volume={21}, number={5}, year={2024} } -
Enriched Galerkin Discretization for Modelling Poroelasticity and Permeability Alteration in Heterogeneous Porous MediaJournal of Computational Physics, Volume 427, 15 February 2021, 110030.
BibTeX
@article{KADEETHUM2021110030, title = {Enriched Galerkin discretization for modeling poroelasticity and permeability alteration in heterogeneous porous media}, journal = {Journal of Computational Physics}, volume = {427}, pages = {110030}, year = {2021}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2020.110030}, url = {https://www.sciencedirect.com/science/article/pii/S0021999120308044}, author = {T. Kadeethum and H.M. Nick and S. Lee and F. Ballarin}, keywords = {Deformable porous media, Poroelastic effects, Biot's system, Enriched Galerkin, Finite element method, Heterogeneity}, abstract = {In this paper, we utilize the enriched Galerkin (EG) finite element method for the flow equation in Biot's system, which provides a robust locally conservative flux in heterogeneous porous media. The computational algorithm to solve the coupled system with the permeability alteration is presented with the linearization and Picard's iterative scheme. The block structure is utilized for the linear system in numerical discretization, and the computer code is shared in the open-source platform. In the numerical experiments, we compare the proposed EG method with the classical continuous Galerkin (CG) and discontinuous Galerkin (DG) finite element methods in different scenarios, including the North sea reservoirs setup. While DG and EG methods provide similar approximations for the pressure solutions, the CG method produces spurious oscillations in fluid pressure and volumetric strain solutions near the material interfaces, especially for the soft materials. The difference of flux approximation between EG and DG methods is insignificant; still, the EG method demands approximately two and three times fewer degrees of freedom than the DG method for two- and three-dimensional geometries.} } -
Quasi-Static Anti-Plane Shear Crack Propagation in a New Class of Nonlinear Strain-Limiting Elastic Solids using Phase-Field RegularizationInternational Journal of Fracture,Volume 227, pages 153-172, (2021).
BibTeX
@article{yoon2021quasi, title={Quasi-static anti-plane shear crack propagation in nonlinear strain-limiting elastic solids using phase-field approach}, author={Yoon, Hyun C and Lee, Sanghyun and Mallikarjunaiah, SM}, journal={International Journal of Fracture}, volume={227}, number={2}, pages={153--172}, year={2021}, publisher={Springer} } -
Hydraulic Fracture Propagation Simulations in Porous Media with Natural Fractures by IPACSUnconventional Resources Technology Conference, 20-22 July 2020. Unconventional Resources Technology Conference (URTeC)
BibTeX
@inproceedings{wheeler2020hydraulic, title={Hydraulic Fracture Propagation Simulations in Porous Media with Natural Fractures by IPACS}, author={Wheeler, Mary F and Lee, Sanghyun}, booktitle={Unconventional Resources Technology Conference, 20--22 July 2020}, pages={793--798}, year={2020}, organization={Unconventional Resources Technology Conference (URTeC)} } -
Finite Element Solvers for Biot's Poroelasticity Equations in Porous MediaMathematical Geosciences, 2020.
BibTeX
@article{kadeethum2020finite, title={Finite element solvers for Biot’s poroelasticity equations in porous media}, author={Kadeethum, Teeratorn and Lee, S and Nick, HM}, journal={Mathematical Geosciences}, volume={52}, number={8}, pages={977--1015}, year={2020}, publisher={Springer} } -
Continuous Galerkin and enriched Galerkin methods with arbitrary order discontinuous trial functions for the elliptic and parabolic problems with jump conditionsJournal of Scientific Computing, 84, 9 (2020).
BibTeX
@article{rupp2020continuous, title={Continuous Galerkin and enriched Galerkin methods with arbitrary order discontinuous trial functions for the elliptic and parabolic problems with jump conditions}, author={Rupp, Andreas and Lee, Sanghyun}, journal={Journal of Scientific Computing}, volume={84}, number={1}, pages={9}, year={2020}, publisher={Springer} } -
IPACS: Integrated Phase‑Field Advanced Crack Propagation Simulator. An adaptive, parallel, physics-based-discretization phase‑field framework for fracture propagation in porous mediaComputer Methods in Applied Mechanics and Engineering, 367 (2020) 113124.
BibTeX
@article{WHEELER2020113124, title = {IPACS: Integrated Phase-Field Advanced Crack Propagation Simulator. An adaptive, parallel, physics-based-discretization phase-field framework for fracture propagation in porous media}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {367}, pages = {113124}, year = {2020}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2020.113124}, url = {https://www.sciencedirect.com/science/article/pii/S0045782520303091}, author = {Mary F. Wheeler and Thomas Wick and Sanghyun Lee}, keywords = {Phase-field fracture, Porous media, Computer implementation, Numerical simulations, Handbook, IPACS}, abstract = {In this work, we review and describe our computational framework for solving multiphysics phase-field fracture problems in porous media. Therein, the following five coupled nonlinear physical models are addressed: displacements (geo-mechanics), a phase-field variable to indicate the fracture position, a pressure equation (to describe flow), a proppant concentration equation, and/or a saturation equation for two-phase fracture flow, and finally a finite element crack width problem. The overall coupled problem is solved with a staggered solution approach, known in subsurface modeling as the fixed-stress iteration. A main focus is on physics-based discretizations. Galerkin finite elements are employed for the displacement-phase-field system and the crack width problem. Enriched Galerkin formulations are used for the pressure equation. Further enrichments using entropy-vanishing viscosity are employed for the proppant and/or saturation equations. A robust and efficient quasi-monolithic semi-smooth Newton solver, local mesh adaptivity, and parallel implementations allow for competitive timings in terms of the computational cost. Our framework can treat two- and three-dimensional realistic field and laboratory examples. The resulting program is an in-house code named IPACS (Integrated Phase-field Advanced Crack Propagation Simulator) and is based on the finite element library deal.II. Representative numerical examples are included in this document.} } -
Flow in porous media with low dimensional fractures by employing enriched Galerkin methodAdvances in Water Resources, 142 (Aug 2020) 103620.
BibTeX
@article{KADEETHUM2020103620, title = {Flow in porous media with low dimensional fractures by employing enriched Galerkin method}, journal = {Advances in Water Resources}, volume = {142}, pages = {103620}, year = {2020}, issn = {0309-1708}, doi = {https://doi.org/10.1016/j.advwatres.2020.103620}, url = {https://www.sciencedirect.com/science/article/pii/S0309170819312576}, author = {T. Kadeethum and H.M. Nick and S. Lee and F. Ballarin}, keywords = {Fractured porous media, Mixed-dimensional, Enriched Galerkin, Finite element method, Heterogeneity, Local mass conservative}, abstract = {This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.} } -
Modeling interactions of natural and two phase fluid filled fracture propagation in porous mediaComputational Geosciences, Volume 25, pages 731-755, (2021)
BibTeX
@article{lee2021modeling, title={Modeling interactions of natural and two-phase fluid-filled fracture propagation in porous media}, author={Lee, Sanghyun and Wheeler, Mary F}, journal={Computational Geosciences}, volume={25}, number={2}, pages={731--755}, year={2021}, publisher={Springer} } -
Optimal error estimate of elliptic problems with Dirac sources for discontinuous and enriched Galerkin methodsApplied Numerical Mathematics, 150 (Apr 2020), 76-104.
BibTeX
@article{CHOI202076, title = {Optimal error estimate of elliptic problems with Dirac sources for discontinuous and enriched Galerkin methods}, journal = {Applied Numerical Mathematics}, volume = {150}, pages = {76-104}, year = {2020}, issn = {0168-9274}, doi = {https://doi.org/10.1016/j.apnum.2019.09.010}, url = {https://www.sciencedirect.com/science/article/pii/S0168927419302491}, author = {Woocheol Choi and Sanghyun Lee}, keywords = {Singularity, Dirac source, Discontinuous Galerkin finite element methods, Enriched Galerkin finite element methods, A priori estimates}, abstract = {We present an optimal a priori error estimates of the elliptic problems with Dirac sources away from the singular point using discontinuous and enriched Galerkin finite element methods. It is widely shown that the finite element solutions for elliptic problems with Dirac source terms converge sub-optimally in classical norms on uniform meshes. However, here we employ inductive estimates and L2 norm to obtain the optimal order by excluding the small ball regions with the singularities for both two and three dimensional domains. Numerical examples are presented to substantiate our theoretical results.} } -
Comparison of Two- and Three-field Formulation Discretizations for Flow and Solid Deformation in Heterogeneous Porous MediaIAMG 2019.
BibTeX
@inproceedings{kadeethum2019comparison, title={Comparison of two-and three-field formulation discretizations for flow and solid deformation in heterogeneous porous media}, author={Kadeethum, Teeratorn and Nick, Hamid and Lee, S}, booktitle={20th Annual Conference of the International Association for Mathematical Geosciences}, year={2019} } -
A Novel Enriched Galerkin Method for Modelling Coupled Flow and Mechanical Deformation in Heterogeneous Porous MediaARMA 2019.
BibTeX
@inproceedings{kadeethum2019novel, title={A novel enriched galerkin method for modelling coupled mechanical deformation in heterogeneous porous media}, author={Kadeethum, Teeratorn and Nick, HM and Lee, S and Richardson, CN and Salimzadeh, S and Ballarin, F}, booktitle={ARMA US Rock Mechanics/Geomechanics Symposium}, pages={ARMA--2019}, year={2019}, organization={ARMA} } -
Numerical Simulation of Matrix Acidizing in Fractured Carbonate Reservoirs Using Adaptive Enriched Galerkin MethodSPE-193862-MS, SPE RSC 2019.
BibTeX
@proceedings{10.2118/193862-MS, author = {Dong, Rencheng and Lee, Sanghyun and Wheeler, Mary }, title = {Numerical Simulation of Matrix Acidizing in Fractured Carbonate Reservoirs Using Adaptive Enriched Galerkin Method}, volume = {SPE Reservoir Simulation Conference}, series = {SPE Reservoir Simulation Conference}, pages = {D021S010R001}, year = {2019}, month = {04}, abstract = {Acidizing in un-fractured carbonate reservoirs has been well studied through modeling and simulation. Since carbonate reservoirs are often naturally fractured, fractures should be modeled for realistic acidizing operations. We present adaptive enriched Galerkin (EG) methods to simulate acidizing in fractured carbonate reservoirs. We adopt a two-scale continuum model for the acid transport. The coupled flow and reactive transport systems are spatially discretized by EG methods. Fractures are introduced using local grid refinement (LGR) technique. Adaptive mesh refinement (AMR) is implemented around wormhole interfaces. Simulation results show that acidizing in fractured carbonate reservoirs is largely dependent on the fracture system while acidizing in unfractured carbonate reservoirs is mainly determined by operation parameters such as acid injection rate. Computationally, the proposed EG scheme has less numerical dispersion and grid orientation effects than standard cell center finite difference/volume methods. AMR is very efficient to track the wormhole growth and speed up acidizing simulations.}, doi = {10.2118/193862-MS}, url = {https://doi.org/10.2118/193862-MS}, eprint = {https://onepetro.org/spersc/proceedings-pdf/19RSC/19RSC/D021S010R001/1164178/spe-193862-ms.pdf}, } -
Unconventional Reservoir Management Modeling Coupling Diffusive Zone/Phase Field Fracture Modeling and Fracture Probability MapsSPE 193830-MS, SPE RSC 2019.
BibTeX
@inproceedings{wheeler2019unconventional, title={Unconventional reservoir management modeling coupling diffusive zone/phase field fracture modeling and fracture probability maps}, author={Wheeler, Mary F and Srinivasan, Sanjay and Lee, Sanghyun and Singh, Manik}, booktitle={SPE Reservoir Simulation Conference}, pages={D021S014R004}, year={2019}, organization={SPE} } -
The effect of stress boundary conditions on fluid-driven fracture propagation in porous media using a phase field modeling approachInternational Journal for Numerical and Analytical Methods in Geomechanics, 43(6):1316-1340 (2019).
BibTeX
@article{shiozawa2019effect, title={The effect of stress boundary conditions on fluid-driven fracture propagation in porous media using a phase-field modeling approach}, author={Shiozawa, Sogo and Lee, Sanghyun and Wheeler, Mary F}, journal={International Journal for Numerical and Analytical Methods in Geomechanics}, volume={43}, number={6}, pages={1316--1340}, year={2019}, publisher={Wiley Online Library} } -
Enriched Galerkin Finite Element Method for Locally Mass Conservative Simulation of Coupled Hydromechanical ProblemsChina‑Europe Conf. on Geotechnical Engineering (2018).
BibTeX
@inproceedings{choo2018enriched, title={Enriched Galerkin Finite Element Method for Locally Mass Conservative Simulation of Coupled Hydromechanical Problems}, author={Choo, Jinhyun and Lee, Sanghyun}, booktitle={Proceedings of China-Europe Conference on Geotechnical Engineering: Volume 1}, pages={312--315}, year={2018}, organization={Springer} } -
Enriched Galerkin finite elements for coupled poromechanics with local mass conservationComputer Methods in Applied Mechanics and Engineering, 341 (2018) 311-332.
BibTeX
@article{CHOO2018311, title = {Enriched Galerkin finite elements for coupled poromechanics with local mass conservation}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {341}, pages = {311-332}, year = {2018}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2018.06.022}, url = {https://www.sciencedirect.com/science/article/pii/S0045782518303207}, author = {Jinhyun Choo and Sanghyun Lee}, keywords = {Enriched Galerkin method, Finite element method, Coupled poromechanics, Local mass conservation}, abstract = {Robust and efficient discretization methods for coupled poromechanical problems are critical to address a wide range of problems related to civil infrastructure, energy resources, and environmental sustainability. In this work, we propose a new finite element formulation for coupled poromechanical problems that ensures local (element-wise) mass conservation. The proposed formulation draws on the so-called enriched Galerkin method, which augments piecewise constant functions to the classical continuous Galerkin finite element method. These additional degrees of freedom allow us to obtain a locally conservative and nonconforming solution for the pore pressure field. The enriched and continuous Galerkin formulations are compared in several numerical examples ranging from a benchmark consolidation problem to a complex problem that involves plastic deformation due to unsaturated flow in a heterogeneous porous medium. The results of these examples show not only that the proposed method provides local mass conservation, but also that local mass conservation can be crucial to accurate simulation of deformation processes in fluid-infiltrated porous materials.} } -
Enriched Galerkin approximations for two phase flow in porous media with capillary pressureJournal of Computational Physics, 367 (2018) 65-86.
BibTeX
@article{LEE201865, title = {Enriched Galerkin methods for two-phase flow in porous media with capillary pressure}, journal = {Journal of Computational Physics}, volume = {367}, pages = {65-86}, year = {2018}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2018.03.031}, url = {https://www.sciencedirect.com/science/article/pii/S0021999118301918}, author = {Sanghyun Lee and Mary F. Wheeler}, keywords = {Enriched Galerkin finite element methods, Two-phase flow, Capillary pressure, Porous media, Entropy viscosity, Dynamic mesh adaptivity}, abstract = {In this paper, we propose an enriched Galerkin (EG) approximation for a two-phase pressure saturation system with capillary pressure in heterogeneous porous media. The EG methods are locally conservative, have fewer degrees of freedom compared to discontinuous Galerkin (DG), and have an efficient pressure solver. To avoid non-physical oscillations, an entropy viscosity stabilization method is employed for high order saturation approximations. Entropy residuals are applied for dynamic mesh adaptivity to reduce the computational cost for larger computational domains. The iterative and sequential IMplicit Pressure and Explicit Saturation (IMPES) algorithms are treated in time. Numerical examples with different relative permeabilities and capillary pressures are included to verify and to demonstrate the capabilities of EG.} } -
Phase-field modeling of two phase fluid-filled fractures in a poroelastic mediumMultiscale Modeling & Simulation, 16(4):1542-1580 (2018).
BibTeX
@article{lee2018phase, title={Phase-field modeling of two phase fluid filled fractures in a poroelastic medium}, author={Lee, Sanghyun and Mikelic, Andro and Wheeler, Mary F and Wick, Thomas}, journal={Multiscale Modeling \& Simulation}, volume={16}, number={4}, pages={1542--1580}, year={2018}, publisher={SIAM} } -
Optimal design of hydraulic fracturing in porous media using the phase field fracture model coupled with genetic algorithmComputational Geosciences, 22(3):833-849 (2018).
BibTeX
@article{lee2018optimal, title={Optimal design of hydraulic fracturing in porous media using the phase field fracture model coupled with genetic algorithm}, author={Lee, Sanghyun and Min, Baehyun and Wheeler, Mary F}, journal={Computational Geosciences}, volume={22}, number={3}, pages={833--849}, year={2018}, publisher={Springer} } -
Multirate Coupling for Flow and Geomechanics Applied to Hydraulic Fracturing Using an Adaptive Phase‑Field TechniqueSPE-182610-MS, SPE Reservoir Simulation Conference (2017).
BibTeX
@inproceedings{almani2017multirate, title={Multirate coupling for flow and geomechanics applied to hydraulic fracturing using an adaptive phase-field technique}, author={Almani, Tameem and Lee, Sanghyun and Wheeler, Mary F and Wick, Thomas}, booktitle={SPE Reservoir Simulation Conference}, pages={D031S010R001}, year={2017}, organization={SPE} } -
Analytical and variational numerical methods for unstable miscible displacement flows in porous mediaJournal of Computational Physics, 335 (2017) 444-496.
BibTeX
@article{SCOVAZZI2017444, title = {Analytical and variational numerical methods for unstable miscible displacement flows in porous media}, journal = {Journal of Computational Physics}, volume = {335}, pages = {444-496}, year = {2017}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2017.01.021}, url = {https://www.sciencedirect.com/science/article/pii/S0021999117300311}, author = {Guglielmo Scovazzi and Mary F. Wheeler and Andro MikeliÄ and Sanghyun Lee}, keywords = {Miscible displacement, Viscous fingering, Flow instabilities, Hele-Shaw, Variational methods, Numerical simulation, Galerkin methods}, abstract = {The miscible displacement of one fluid by another in a porous medium has received considerable attention in subsurface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patterns â referred to as viscous fingering â may arise. Their physical and mathematical study has been the object of numerous investigations over the past century. The objective of this paper is to present a review of these contributions with particular emphasis on variational methods. These algorithms are tailored to real field applications thanks to their advanced features: handling of general complex geometries, robustness in the presence of rough tensor coefficients, low sensitivity to mesh orientation in advection dominated scenarios, and provable convergence with fully unstructured grids. This paper is dedicated to the memory of Dr. Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods.} } -
Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilizationJournal of Computational Physics, 331 (2017) 19-37.
BibTeX
@article{LEE201719, title = {Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization}, journal = {Journal of Computational Physics}, volume = {331}, pages = {19-37}, year = {2017}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2016.10.072}, url = {https://www.sciencedirect.com/science/article/pii/S0021999116305952}, author = {Sanghyun Lee and Mary F. Wheeler}, keywords = {Enriched Galerkin finite element methods, Miscible displacement, Viscous fingering, Locally conservative methods, Entropy viscosity, HeleâShaw}, abstract = {We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and HeleâShaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.} } -
Iterative coupling of flow, geomechanics and adaptive phase‑field fracture including a level-set crack width approachJournal of Computational and Applied Mathematics, 314 (2017) 40-60.
BibTeX
@article{LEE201740, title = {Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approaches}, journal = {Journal of Computational and Applied Mathematics}, volume = {314}, pages = {40-60}, year = {2017}, issn = {0377-0427}, doi = {https://doi.org/10.1016/j.cam.2016.10.022}, url = {https://www.sciencedirect.com/science/article/pii/S0377042716305118}, author = {Sanghyun Lee and Mary F. Wheeler and Thomas Wick}, keywords = {Fluid-filled phase field fracture, Fixed stress splitting, Pressure diffraction equation, Level-set method, Crack width, Porous media}, abstract = {In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension to fixed-stress splitting to propagating phase-field fractures and systematic investigation of its properties are important enhancements to existing studies. Moreover, we provide an accurate computation of the fracture opening using level-set approaches and a subsequent finite element interpolation of the width. The latter enters as fracture permeability into the pressure diffraction problem which is crucial for fluid filled fractures. Our developments are substantiated with several numerical tests that include comparisons of computational cost for iterative coupling and nonlinear and linear iterations as well as convergence studies in space and time.} } -
Investigation of wing crack formation with a combined phase-field and experimental approachGeophysical Research Letters, 43:7946-7952 (2016).
BibTeX
@article{LeeReber_2016, author = {Lee, Sanghyun and Reber, Jacqueline E. and Hayman, Nicholas W. and Wheeler, Mary F.}, title = {Investigation of wing crack formation with a combined phase-field and experimental approach}, journal = {Geophysical Research Letters}, volume = {43}, number = {15}, pages = {7946-7952}, keywords = {wing crack, model benchmark, phase-field model, gelatine experiments}, doi = {https://doi.org/10.1002/2016GL069979}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2016GL069979}, eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016GL069979}, abstract = {Abstract Fractures that propagate off of weak slip planes are known as wing cracks and often play important roles in both tectonic deformation and fluid flow across reservoir seals. Previous numerical models have produced the basic kinematics of wing crack openings but generally have not been able to capture fracture geometries seen in nature. Here we present both a phase-field modeling approach and a physical experiment using gelatin for a wing crack formation. By treating the fracture surfaces as diffusive zones instead of as discontinuities, the phase-field model does not require consideration of unpredictable rock properties or stress inhomogeneities around crack tips. It is shown by benchmarking the models with physical experiments that the numerical assumptions in the phase-field approach do not affect the final model predictions of wing crack nucleation and growth. With this study, we demonstrate that it is feasible to implement the formation of wing cracks in large scale phase-field reservoir models.}, year = {2016} } -
Stability analysis of pressure correction schemes for the Navier-Stokes equations with traction boundary conditionsComputer Methods in Applied Mechanics and Engineering, 309 (2016) 307-324.
BibTeX
@article{LEE2016307, title = {Stability analysis of pressure correction schemes for the NavierâStokes equations with traction boundary conditions}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {309}, pages = {307-324}, year = {2016}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2016.05.043}, url = {https://www.sciencedirect.com/science/article/pii/S0045782516304923}, author = {Sanghyun Lee and Abner J. Salgado}, keywords = {NavierâStokes, Open and traction boundary conditions, Fractional time stepping}, abstract = {We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the gradâdiv stabilized scheme of Bonito et al. (2015). This scheme turns out to be unconditionally stable, provided the stabilization parameter is suitably chosen. We also establish a conditional stability result for the boundary correction scheme presented in BÀnsch (2014). These results are shown by employing the equivalence between stabilized gauge Uzawa methods and rotational pressure correction schemes with traction boundary conditions.} } -
Initialization of phase-field fracture propagation in porous media using probability maps of fracture networksMechanics Research Communications, 80 (2017) 16-23.
BibTeX
@article{LEE201716, title = {Initialization of phase-field fracture propagation in porous media using probability maps of fracture networks.}, journal = {Mechanics Research Communications}, volume = {80}, pages = {16-23}, year = {2017}, note = {Multi-Physics of Solids at Fracture}, issn = {0093-6413}, doi = {https://doi.org/10.1016/j.mechrescom.2016.04.002}, url = {https://www.sciencedirect.com/science/article/pii/S0093641316300106}, author = {Sanghyun Lee and Mary F. Wheeler and Thomas Wick and Sanjay Srinivasan}, keywords = {Hydraulic fracturing, Probability map, Phase-field fracture formulation}, abstract = {It is well known in the geophysical community that surface deflection information/micro-seismic data are considered to be one of the best diagnostics for revealing the volume of rock fracture. However, the in-exactness of the data representing the deformation induced to calibrate and represent complex fracture networks created and connected during hydraulic fracturing presents a challenge. In this paper, we propose a technique that implements a phase-field approach to propagate fractures and their interaction with existing fracture networks using surface deflection data. The latter one provides a probability map of fractures in a heterogeneous reservoir. These data are used to initialize both the location of the fractures and the phase-field function. In addition, this approach has the potential for optimizing well placement/spacing for fluid-filled fracture propagation for oil and gas production and or carbon sequestration and utilization. Using prototype models based on realistic field data, we demonstrate the effects of interactions between existing and propagating fractures in terms of several numerical simulations with different probability thresholds, locations, and numbers of fractures. Our results indicate that propagating fractures interact in a complex manner with the existing fracture network. The modeled propagation of hydraulic fractures is sensitive to the threshold employed within the phase-field approach for delineating fractures.} } -
A Locally Conservative Enriched Galerkin Approximation and Efficient Solver for the Parabolic ProblemsSIAM Journal on Scientific Computing, 38(3):A1404-A1429 (2016).
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Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field modelComputer Methods in Applied Mechanics and Engineering, 305 (2016) 111-132.
BibTeX
@article{LEE2016111, title = {Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {305}, pages = {111-132}, year = {2016}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2016.02.037}, url = {https://www.sciencedirect.com/science/article/pii/S0045782516300676}, author = {Sanghyun Lee and Mary F. Wheeler and Thomas Wick}, keywords = {Phase field, Fluid filled fracture, Adaptive finite elements, Porous media, Primalâdual active set}, abstract = {This work presents phase field fracture modeling in heterogeneous porous media. We develop robust and efficient numerical algorithms for pressure-driven and fluid-driven settings in which the focus relies on mesh adaptivity in order to save computational cost for large-scale 3D applications. In the fluid-driven framework, we solve for three unknowns pressure, displacements and phase field that are treated with a fixed-stress iteration in which the pressure and the displacementâphase-field system are decoupled. The latter subsystem is solved with a combined Newton approach employing a primalâdual active set method in order to account for crack irreversibility. Numerical examples for pressurized fractures and fluid filled fracture propagation in heterogeneous porous media demonstrate our developments. In particular, mesh refinement allows us to perform systematic studies with respect to the spatial discretization parameter.} } -
Phase‑field modeling of proppant-filled fractures in a poroelastic mediumComputer Methods in Applied Mechanics and Engineering, 312 (2016) 509-541.
BibTeX
@article{LEE2016509, title = {Phase-field modeling of proppant-filled fractures in a poroelastic medium}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {312}, pages = {509-541}, year = {2016}, note = {Phase Field Approaches to Fracture}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2016.02.008}, url = {https://www.sciencedirect.com/science/article/pii/S0045782516300305}, author = {Sanghyun Lee and Andro MikeliÄ and Mary F. Wheeler and Thomas Wick}, keywords = {Phase field fracture, Hydraulic fracturing, Proppant transport, Quasi-Newtonian flow model}, abstract = {In this paper we present a phase field model for proppant-filled fractures in a poroelastic medium. The formulation of the coupled system involves four unknowns: displacements, phase field, pressure, and proppant concentration. The two-field displacement phase-field system is solved fully-coupled and accounts for crack irreversibility. This solution is then coupled to the pressure equation via a fixed-stress iteration. The pressure is obtained by using a diffraction equation where the phase-field variable serves as an indicator function that distinguishes between the fracture and the reservoir. The transport of the proppant in the fracture is modeled by using a power-law fluid system. The numerical discretization in space is based on Galerkin finite elements for displacements and phase-field, and an enriched Galerkin method is applied for the pressure equation in order to obtain local mass conservation. The concentration is solved with cell-centered finite elements. Nonlinear equations are treated with Newtonâs method. Our developments are substantiated with several numerical examples in two and three dimensions.} } -
3D Phase-field for pressurized fracture propagation in heterogeneous mediaProceedings of VI Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering (2015).
BibTeX
@inproceedings{wick20153d, title={3D phase-field for pressurized fracture propagation in heterogeneous media}, author={Wick, Thomas and Lee, Sanghyun and Wheeler, Mary F}, booktitle={COUPLED VI: Proceedings of the VI International Conference on Computational Methods for Coupled Problems in Science and Engineering}, pages={605--613}, year={2015}, organization={CIMNE} } -
Numerical Simulations of Bouncing JetsInternational Journal for Numerical Methods in Fluids, 80 (2016) 53-75.
BibTeX
@article{BonitoLee_2016, author = {Bonito, Andrea and Guermond, Jean-Luc and Lee, Sanghyun}, title = {Numerical simulations of bouncing jets}, journal = {International Journal for Numerical Methods in Fluids}, volume = {80}, number = {1}, pages = {53-75}, keywords = {bouncing jet, Kaye effect, entropy viscosity, level set, projection method, shear-thinning viscosity, adaptive finite elements}, doi = {https://doi.org/10.1002/fld.4071}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.4071}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.4071}, abstract = {Summary Bouncing jets are fascinating phenomenon occurring under certain conditions when a jet impinges on a free surface. This effect is observed when the fluid is Newtonian and the jet falls in a bath undergoing a solid motion. It occurs also for non-Newtonian fluids when the jets fall in a vessel at rest containing the same fluid. We investigate numerically the impact of the experimental setting and the rheological properties of the fluid on the onset of the bouncing phenomenon. Our investigations show that the occurrence of a thin lubricating layer of air separating the jet and the rest of the liquid is a key factor for the bouncing of the jet to happen. The numerical technique that is used consists of a projection method for the Navier–Stokes system coupled with a level set formulation for the representation of the interface. The space approximation is carried out with adaptive finite elements. Adaptive refinement is shown to be very important to capture the thin layer of air that is responsible for the bouncing. Copyright © 2015 John Wiley \& Sons, Ltd.}, year = {2016} } -
Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time SteppingENUMATH 2013, Lecture Notes in Computational Science and Engineering 103 (2015) 623-631.
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Leaping shampoo glides on a lubricating layerPhysical Review E (Rapid Communication), 87(6) (2013).
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Ph.D. Thesis
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Numerical Simulations of Bouncing JetsPh.D. Thesis, Texas A\&M University (2014).
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