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Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systemsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Dumbser Michael, Käser Martin, Titarev Vladimir A., Toro Eleuterio F.
- Журнал: Journal of Computational Physics
- Том: 226
- Номер: 1
- Год издания: 2007
- Издательство: Academic Press
- Местоположение издательства: United States
- Первая страница: 204
- Последняя страница: 243
- DOI: 10.1016/j.jcp.2007.04.004
- Аннотация: In this article we present a quadrature-free essentially non-oscillatory finite volume scheme of arbitrary high order ofaccuracy both in space and time for solving nonlinear hyperbolic systems on unstructured meshes in two and three spacedimensions. For high order spatial discretization, a WENO reconstruction technique provides the reconstruction polynomials in terms of a hierarchical orthogonal polynomial basis over a reference element. The Cauchy–Kovalewski procedureapplied to the reconstructed data yields for each element a space–time Taylor series for the evolution of the state and thephysical fluxes. This Taylor series is then inserted into a special numerical flux across the element interfaces and is subsequently integrated analytically in space and time. Thus, the Cauchy–Kovalewski procedure provides a natural, direct andcost-efficient way to obtain a quadrature-free formulation, avoiding the expensive numerical quadrature arising usually forhigh order finite volume schemes in three space dimensions. We show numerical convergence results up to sixth order ofaccuracy in space and time for the compressible Euler equations on triangular and tetrahedral meshes in two and threespace dimensions. Furthermore, various two- and three-dimensional test problems with smooth and discontinuous solutions are computed to validate the approach and to underline the non-oscillatory shock-capturing properties of themethod.
- Добавил в систему: Титарев Владимир Александрович