MENU

You are here

A high-order discontinuous Galerkin solver for turbulent incompressible flow

Speaker: 
Martin Kronbichler
Institution: 
Technical University of Munich
Schedule: 
Wednesday, May 17, 2017 - 16:00
Location: 
A-133
Abstract: 

This talk presents recent work in my group regarding the development of a high-order discontinuous Galerkin solver for the incompressible Navier-Stokes equations. For discretization in time, a dual splitting method is used that separately advances the convective term, the incompressibility constraint, and the viscous terms. The most expensive part in this scheme is the solution of a pressure Poisson equation forced by the divergence of the intermediate velocity field after the convective step, for which a state-of-the-art geometric multigrid scheme is used. The spatial discretization uses the Lax-Friedrichs flux for the convective term and the symmetric interior penalty method for the second-derivative terms in the pressure Poisson equation and the viscous term. For application to implicit large eddy simulation of turbulent flow which is marginally resolved per definition, previous incompressible DG codes have suffered from bad stability. In our work, we have addressed these issues by suitable DG formulations of the divergence term on the right hand side of the pressure equation and in the discretization of the pressure gradient in the projection step, based on central fluxes. Furthermore, a consistent div-div penalty term is introduced that suppresses local divergence errors of the magnitude of the discretization error. It is similar to the widely used grad-div stabilization in continuous finite elements. This stabilization also acts as an implicit turbulence model. Applications of the solver to implicit LES of turbulent flow in channel and over a periodic hill as well as function enrichment in RANS simulations show the capabilities of the solver. The enrichment is inspired by wall models in turbulence but provided as a component of the function space in a Galerkin scheme. This construction allows the method to adapt to the local flow features, which makes it robust also for flow with separation and other complex scenarios where classical wall models fail.

Sign in