Space-time discontinuous Galerkin method for the numerical simulation of viscous compressible gas flow with the k-omega turbulence model

Jan Česenek,P Dančová

doi:10.1051/epjconf/201818002016

Abstract

In this article we deal with the numerical simulation of the non-stationary compressible turbulent flow described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. The discretization of these two systems is carried out separately by the space-time discontinuous Galerkin method. This method is based on the piecewise polynomial discontinuous approximation of the sought solution in space and in time. We use the numerical experiments to demonstrate the applicability of the shown approach. All presented results were computed with the own-developed code.

Highlights

During the last decade the space-time discontinuous Galerkin finite element method (ST-DG), which is based on piecewise polynomial discontinuous approximations of the sought solution, became very popular in the field of numerical simulation of the fluid flow
In the case of compressible turbulent flow the finite volume - space-time discontinuous Galerkin method was used [7–9], where the equations of the turbulence model were discretized by the implicit finite volume method
This article is devoted to the discretization of viscous compressible turbulent gas flow using STDG applied for the equations of the turbulence model

Summary

Introduction

During the last decade the space-time discontinuous Galerkin finite element method (ST-DG), which is based on piecewise polynomial discontinuous approximations of the sought solution, became very popular in the field of numerical simulation of the fluid flow. This method of higher order was successfully used for the simulation of the NavierStokes equations [1–6]. In the case of compressible turbulent flow the finite volume - space-time discontinuous Galerkin method was used [7–9], where the equations of the turbulence model were discretized by the implicit finite volume method.

Space discretization of the problem

Full space-time DG discretization

Numerical experiments

Conclusion