Large Eddy Simulation in the Split Form Discontinuous Galerkin Method for the Compressible Navier-Stokes

Download or read book Large Eddy Simulation in the Split Form Discontinuous Galerkin Method for the Compressible Navier-Stokes written by Anthony P. Edmonds and published by . This book was released on 2020 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discontinuous Galerkin (DG) method is a finite element method. The method is computationally efficient, scalable in parallel, and is capable of handling complex geometries; these attributes make the DG method popular for solving the Navier-Stokes equations .Traditional DG formulations utilize the weak form of the conservative equations, whereas there is a discretization that utilizes the strong formulation of these equations: this is called the split-form discretization. The goal of this work is to study large eddy simulation (LES) in the split-form discretization and contrast it with the standard weak form DG discretization. An explicit filtering operation is required for LES using a dynamic sub-grid scale (SGS) model referred to as the dynamic Smagorisnky model. Two modes of filtering were explored: a polynomial cutoff filter and a Laplacian filter. The polynomial cutoff filter works by removing high order modes. The high-order modes correspond to the high-order energy content of the solution. The Laplacian filter applies the Laplace operator to smooth out areas of the flow with large gradients. These areas correspond to this high-order energy content. The dynamic Smagorisnky model is analyzed along side the constant Smagorisnky model. The models were analyzed using the Taylor-Green vortex (TGV) problem. The TGV initially is laminar but then transitions to fully turbulent flow. This is an ideal candidate for studying the sub-grid scale (SGS) models used in LES; as this transition is a challenge. The constant Smagorisnky model is overly dissipative, and under predicts kinetic energy. The dynamic model performs better, however is far more costly to calculate. The split-form discretization is more dissipative than the standard DG formulation, however it is far more stable.