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Murtazo Nazarov: Stabilized finite element methods for fluid problems

Time: Thu 2019-11-21 15.30 - 16.15

Location: Kräftriket, house 6, room 306 (Cramér-rummet)

Participating: Murtazo Nazarov, Uppsala University

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The finite element method is known to be unstable for advection dominated problems, such as fluid dynamics, atmospheric flows, thermodynamics, magnetohydrodynamics, etc. To cure this problem many stabilization techniques based on the Least-Squares (Galerkin-Least-Squares GLS, Streamline-Upwind-Petrov-Galerkin SUPG, Edge stabilization, and many others) were proposed since the early '80s. These methods are counted as the state-of-the-art approximations for fluid flow using finite elements. In this talk, I will discuss some of the limitations of these methods in terms of accuracy, efficiency, and convergence. And then, I will introduce our recent work in this field that is discretization independent, high order, positivity preserving, works for problems with strong shocks and discontinuities and various Mach numbers. I will present several numerical simulations for the compressible flows. Then, I will show the extension of the method to solve the Surface-Quasi-Geostrophic equation, which is used to simulate atmospheric flows. We believe that our approach fits well into the framework of Implicit Large Eddy Simulations for fluid problems.