Abstract
Accurate methods to solve the Reynolds-Averaged Navier-Stokes (RANS) equations coupled to turbulence models are still of great interest, as this is often the only computationally feasible approach to simulate complex turbulent flows in large engineering applications. In this work, we present a novel discontinuous Galerkin (DG) solver for the RANS equations coupled to the k−ϵ model (in logarithmic form, to ensure positivity of the turbulence quantities). We investigate the possibility of modeling walls with a wall function approach in combination with DG. The solver features an algebraic pressure correction scheme to solve the coupled RANS system, implicit backward differentiation formulae for time discretization, and adopts the Symmetric Interior Penalty method and the Lax-Friedrichs flux to discretize diffusive and convective terms respectively. We pay special attention to the choice of polynomial order for any transported scalar quantity and show it has to be the same as the pressure order to avoid numerical instability. A manufactured solution is used to verify that the solution converges with the expected order of accuracy in space and time. We then simulate a stationary flow over a backward-facing step and a Von Kármán vortex street in the wake of a square cylinder to validate our approach.
Highlights
Engineering applications often require the simulation of complex turbulent flows via accurate Computational Fluid Dynamics (CFD) methods
We extend a solver for laminar flows presented in [33] to handle turbulence through the set of incompressible Reynolds-Averaged Navier-Stokes (RANS) equations coupled to the k − model
We have presented a novel high-order discontinuous Galerkin Finite Element (DG-FEM) solver for the incompressible Reynolds-Averaged Navier-Stokes (RANS) equations coupled with the k − closure model
Summary
Engineering applications often require the simulation of complex turbulent flows via accurate Computational Fluid Dynamics (CFD) methods. Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) constitute superior approaches in this regard, as they are able to resolve the stochastic fluctuations (though only the large-scale ones in case of LES) of any turbulent flow quantity [1]. Nowadays they are still very computationally expensive and often unaffordable for large engineering applications. Accurate and efficient numerical methods to solve the RANS equations are still of great relevance. The characteristic feature of DG is that unknown quantities are approximated with polynomial ba-
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