Mathematical Research at FSU
Dr. Hussaini and collaborators develop numerical algorithms for optimization, control, and sensitivity analysis in fluid mechanics (optimal placement of wind turbines, airfoil shape optimization) and power grid network topology. Also numerical algorithms are developed and applied to the fields of Cryogenics, Nano-fluids, Nano-materials, Visualization, Sensing, and Imaging. The numerical algorithm research involves developing high-order compact schemes (such as discontinuous spectral Galerkin/collocation methods for Euler and Navier-Stokes equations and variants thereof) and efficient techniques for stochastic partial differential equations. It includes levelset procedures for front tracking such as shock waves. The work in high-performance computing involves the implementation of these algorithms on parallel platforms such as SP4 and NCSA Xeon Linux Cluster.
Dr. Lee's research includes computational mathematics with high performance computing in the area ofinterdisciplinary multi physics and multi scale real world problems. In particular, free boundary multiphase problems employing projection methods for Navier Stokes systems, big data analytics for extraction of fracture related information in subsurface systems, and advanced computational approaches for modeling fracture propagation by using Biot system and phase field to couple flow andgeomechanics has been studied in his research.
Dr. Moore's research focuses on modeling fluid flows that are encountered in geophysics and biology. He uses both analytical and numerical methods to develop new models, and, as the ultimate test of a mathematical theory, he collaborates with experimentalists to compare his results to the real world.
Dr. Sussman and his group develop numerical algorithms for computing solutions to deforming boundary problems with applications to multiphase flow. Multiphase flow phenomena is important in the fields of ship wave hydrodynamics, underwater explosions/implosions, dispersive bubble/drop motion in Newtonian or Non-Newtonian continuous media, atomization and spray in combustion chambers, freezing on aircraft wings, bubble plumes, and droplet creation in microfluidic devices. Numerical techniques on dynamic adaptive grids for parallel computers are developed. Techniques for deforming boundary problems include level set methods, volume of fluid methods, and more recently, the moment-of-fluid method.
Dr. Tam and his research team developed a new way to discretize partial differential equations into high-order high-resolution time-marching finite difference algorithms using Fourier-Laplace transforms. This approach is radically different from traditional methods that, invariably, are based on truncated Taylor series. The new method leads to what is known as the Dispersion-Relation-Preserving (DRP) schemes. DRP schemes are widely used in solving acoustics, electromagnetics and seismic waves and other wave propagation problems. Current research involves the extension of the DRP scheme to unstructured grids, development of time-domain stochastic boundary conditions, fully absorbing boundary treatment and numerical methods with ultra-high resolution.