期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 45, 期 1-3, 页码 348-358出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-009-9339-4
关键词
High order methods; Discontinuous Galerkin; Spectral difference; Stability proof
资金
- National Science Foundation [0708071, FA9550-07-1-0195]
- Air Force Office of Scientific Research [0708071, FA9550-07-1-0195]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0915006, 0708071] Funding Source: National Science Foundation
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.
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