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

Authors


Correspondence to: Tobias Leicht, German Aerospace Center (DLR), Lilienthalplatz 7, 38108 Braunschweig, Germany.

E-mail: Tobias.Leicht@dlr.de

SUMMARY

We present an eigen-decomposition of the quasi-linear convective flux formulation of the completely coupled Reynolds-averaged Navier–Stokes and 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. Copyright © 2012 John Wiley & Sons, Ltd.

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