Finite volume - space-time discontinuous Galerkin method for the numerical simulation of compressible turbulent flow in time dependent domains

Jan Česenek

doi:10.1051/epjconf/201714302014

Abstract

The article is concerned with the numerical simulation of the compressible turbulent flow in time dependent domains. The mathematical model of flow is represented by the system of non-stationary Reynolds- Averaged Navier-Stokes (RANS) equations. The motion of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the RANS equations. This RANS system is equipped with two-equation k − ω 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 − ω 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

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]). This method became unstable, when it was used for the whole system of the ReynoldsAveraged Navier-Stokes (RANS) equations with k − ω equations
Due to the time dependent domain the RANS equations are transformed in the ALE (Arbitrary Lagrangian-Eulerian) formulation

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.

Space discretization of the flow problem

Full space-time DGM discretization

Equations for the moving airfoil

Numerical experiments