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.
|Advisor:||Mavriplis, Dimitri J.|
|Commitee:||Heinz, Stefan, Stoellinger, Michael K.|
|School:||University of Wyoming|
|School Location:||United States -- Wyoming|
|Source:||MAI 82/7(E), Masters Abstracts International|
|Subjects:||Computational physics, Fluid mechanics, Energy|
|Keywords:||Discontinuous Galerkin, Finite Element Method, Large Eddy Simulation, Smagorisnky Model, Taylor Green Vortex|
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