Finite volume - space-time discontinuous Galerkin method for the solution of compressible turbulent flow

Jan Česenek,P Dančová,M Veselý

doi:10.1051/epjconf/201611402012

Jan Česenek, P Dančová + Show 1 more

Open Access

https://doi.org/10.1051/epjconf/201611402012

Copy DOI

Abstract

In this article we deal with numerical simulation of the non-stationary compressible turbulent flow. Compressible turbulent flow is described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k-omega turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.

Highlights

IntroductionDuring 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
Compressible turbulent flow is described by the Reynolds-Averaged Navier-Stokes (RANS) equations
Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time

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 simulation of the NavierStokes equations ([2],[4],[5]). We use the ST-DG for the discretization of the RANS system of equations and the finite volume method for the equations of the k − ω turbulence model. ∂n ΓO with given data w 0, ωD, kD, ωwall

Space discretization

Full space-time DGM discretization

Numerical experiments

Conclusion