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Numerical flux functions for Reynolds-averaged Navier–Stokes and kω turbulence model computations with a line-preconditioned p-multigrid discontinuous Galerkin solver

Marcel Wallraff , Tobias Leicht and Markus Lange-Hegermann,
Jun 2012

We present an eigen-decomposition of the quasi-linear convective flux formulation of the completely coupled Reynolds-averaged Navier–Stokes and kω turbulence model equations. Based on these results, we formulate different approximate Riemann solvers that can be used as numerical flux functions in a DG discretization. The effect of the different strategies on the solution accuracy is investigated with numerical examples. The actual computations are performed using a p-multigrid algorithm. To this end, we formulate a framework with a backward-Euler smoother in which the linear systems are solved with a general preconditioned Krylov method. We present matrix-free implementations and memory-lean line-Jacobi preconditioners and compare the effects of some parameter choices. In particular, p-multigrid is found to be less efficient than might be expected from recent findings by other authors. This might be due to the consideration of turbulent flow.

Literature procurement: Wiley
@misc{2371,
author= {Wallraff, Marcel and Leicht, Tobias and Lange-Hegermann, Markus},
title= {Numerical flux functions for Reynolds-averaged Navier–Stokes and kω turbulence model computations with a line-preconditioned p-multigrid discontinuous Galerkin solver},
howpublished= {},
month= {Jun},
year= {2012},
note= {},
}