Article

Multigrid Solver Algorithms for DG Methods and Applications to Aerodynamic Flows

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Abstract

In this chapter we collect results obtained within the IDIHOM project on the development of Discontinuous Galerkin (DG) methods and their application to aerodynamic flows. In particular, we present an application of multigrid algorithms to a higher order DG discretization of the Reynolds-averaged Navier-Stokes (RANS) equations in combination with the Spalart-Allmaras as well as the Wilcox-kw turbulence model. Based on either lower order discretizations or agglomerated coarse meshes the resulting solver algorithms are characterized as p- or h-multigrid, respectively. Linear and nonlinear multigrid algorithms are applied to IDIHOM test cases, namely the L1T2 high lift configuration and the delta wing of the second Vortex Flox Experiment (VFE-2) with rounded leading edge. All presented algorithms are compared to a strongly implicit single grid solver in terms of number of nonlinear iterations and computing time. Furthermore, higher order DG methods are combined with adaptive mesh refinement, in particular, with residual-based and adjoint-based mesh refinement. These adaptive methods are applied to a subsonic and transonic flow around the VFE-2 delta wing.

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... Secondly, since a certain Hermite spectral method is employed to derive the moment model from the Boltzmann equation, the present multi-level moment solver would to some extent coincide with the so-called p-multigrid method [13,16] or spectral multigrid method [25,29], which has been successfully applied in various fields, see e.g. [22,24,26,31,33]. Finally, numerical examples carried in the present paper verify that this new idea is indeed able to accelerate the steady-state computation significantly. ...
Preprint
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Article
We study the acceleration of steady-state computation for microflow, which is modeled by the high-order moment models derived recently from the steady-state Boltzmann equation with BGK-type collision term. By using the lower-order model correction, a novel nonlinear multi-level moment solver is developed. Numerical examples verify that the resulting solver improves the convergence significantly thus is able to accelerate the steady-state computation greatly. The behavior of the solver is also numerically investigated. It is shown that the convergence rate increases, indicating the solver would be more efficient, as the total levels increases. Three order reduction strategies of the solver are considered. Numerical results show that the most efficient order reduction strategy would be ml1=ml/2m_{l-1} = \lceil m_{l} / 2 \rceil.
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