Space-time discontinuous Galerkin method for the numerical simulation of the compressible turbulent gas flow through the porous media

Jan Česenek,P Dančová,J Novosad

doi:10.1051/epjconf/201921302011

Abstract

The article is concerned with the numerical simulation of the compressible turbulent gas flow through the porous media using space-time discontinuous Galerkin method.The mathematical model of flow is represented by the system of non-stationary Reynolds-Averaged Navier-Stokes (RANS) equations. The flow through the porous media is characterized by the loss of momentum. 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 present some numerical experiments to demonstrate the applicability of the method using 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
This article is devoted to the discretization of viscous compressible turbulent gas flow through the porous media using ST-DG
The flow is described by the system of the Reynolds-Averaged Navier-Stokes (RANS) equations equipped with the system of k − ω equations

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 Navier-Stokes equations [1–6] or compressible turbulent flow ([7–10]). This article is devoted to the discretization of viscous compressible turbulent gas flow through the porous media using ST-DG. The flow through the porous media is characterized by the loss of momentum in the RANS equations.

Space discretization of the problem

Full space-time DG discretization

Numerical experiments

Conclusion