Stability analysis of the cell centered finite-volume M<Emphasis Type="SmallCaps">uscl</Emphasis> method on unstructured grids |
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Authors: | F Haider J-P Croisille B Courbet |
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Institution: | 1.Département de simulation numérique des écoulements et aéroacoustique,ONERA,Chatillon,France;2.Laboratoire Mathématiques et Applications de Metz,UMR 7122 Université Paul Verlaine-Metz,Metz,France |
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Abstract: | The goal of this study is to apply the Muscl scheme to the linear advection equation on general unstructured grids and to examine the eigenvalue stability of the resulting
linear semi-discrete equation. Although this semi-discrete scheme is in general stable on cartesian grids, numerical calculations
of spectra show that this can sometimes fail for generalizations of the Muscl method to unstructured three-dimensional grids. This motivates our investigation of the influence of the slope reconstruction
method and stencil on the eigenvalue stability of the Muscl scheme. A theoretical stability analysis of the first order upwind scheme proves that this method is stable on arbitrary
grids. In contrast, a general theoretical result is very difficult to obtain for the Muscl scheme. We are able to identify a local property of the slope reconstruction that is strongly related to the appearance of
unstable eigenmodes. This property allows to identify the reconstruction methods that are best suited for stable discretizations.
The explicit numerical computation of spectra for a large number of two- and three-dimensional test cases confirms and completes
the theoretical results. |
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