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JSCIC
2010

A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy

9 years 5 months ago
A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy
While second order methods for computational simulations of fluid flow provide the basis of widely used commercial software, there is a need for higher order methods for more accurate simulations of turbulent and vortex dominated flows. The discontinuous Galerkin (DG) method is the subject of much current research toward this goal. The spectral difference (SD) method has recently emerged as a promising alternative which can reduce the computational costs of higher order simulations. There remains some questions, however, about the stability of the SD method. This paper presents a proof that for the case of one dimensional linear advection the SD method is stable for all orders of accuracy in a norm of Sobolev type, provided that the interior fluxes collocation points are placed at the zeros of the corresponding Legendre polynomial. Keywords High order methods
Antony Jameson
Added 19 May 2011
Updated 19 May 2011
Type Journal
Year 2010
Where JSCIC
Authors Antony Jameson
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