Towards Implicit Large Eddy Simulation of fluid flow using nonlinear stabilization techniques

Time: Wed 2019-05-29 14.00 - 15.00

Lecturer: Murtazo Nazarov (Uppsala University)

Location: Faxen, FPL, Teknikringen 8

Abstract. Most of the Large Eddy Simulation LES methods in continuous finite elements, such as Variational Multiscale (VMS), Streamline-Upwind-Petrov-Galerkin (SUPG), Galerkin Least-Squares (GLS), General Galerkin (G2) are based on the least-squares argument. These methods are introduced in the early 80s and are still counted as the state-of-the-art approximations for fluid flow using finite elements. In this talk, we will discuss some of the limitations of these methods in terms of accuracy, efficiency, and convergence. Then, we introduce our recent work in this field that is discretization independent (for instance it works for finite differences, discontinuous Galerkin and spectral element methods), high-order, positivity preserving, works for problems with strong shocks and discontinuities at various Mach numbers. Because of these characteristics, we believe that our approach fits well into the framework of Implicit LES. We will present several numerical examples for compressible Euler and surface quasi-geostrophic equations.