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Mathematics Colloquium


Title: New spectrally accurate space time algorithms with applications in multi-phase and multi-material flows
Date: Friday, December 7, 2018
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. A novel dynamic, hierarchical, space-time spectrally accurate, numerical algorithm for simulating multi-phase flows is described. These new methods are designed for computer platforms ranging from a single multi-core machine up to an exascale computer. On the finest adaptive level, the coupled level set and moment of fluid interface tracking method robustly tracks complex deforming material boundaries in 2D or 3D in which any number of materials can occupy a given computational cell. On coarser adaptive levels, novel space-time spectral element methods have been developed which have been demonstrated to admit approximations that preserve properties of solutions of Partial Differential Equations without ever explicitly meaning to do so. Our new space-time hierarchical spectral element method automatically refines the grid where under-resolved structures (e.g. shocks, material discontinuities, vortex patches) exist, and uses high order space-time spectral elements on the coarser adaptive levels in order to preserve uniform accuracy throughout the whole computational domain. The motivation for developing these new methods is to better understand the following multi-phase flows: atomization and spray in diesel injectors, atomization and spray in jet engines, boiling in micro-gravity environments or nuclear reactors, ship wave hydrodynamics, multi-phase pipe flow, and thermal management in geared turbofans. This is joint work with Dr. C. Pei, Dr. M. Vahab, and Professor M.Y. Hussaini.