Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 （1988）, pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillat...Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 （1988）, pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillatory （HWENO） methods to solve hyperbolic conservation laws. The key feature of the multi-step temporal discretization procedure is to use variable time step with strong stability preserving （SSP）. The multi-step tem- poral discretization methods can make full use of computed information with HWENO spatial discretization by holding the former computational values. Extensive numerical experiments are presented to demonstrate that the finite volume HWENO schemes with multi-step diseretization can achieve high order accuracy and maintain non-oscillatory properties near discontinuous region of the solution.展开更多
文摘Based on the work of Shu [SIAM J. Sci. Stat. Comput, 9 （1988）, pp.1073-1084], we construct a class of high order multi-step temporal discretization procedure for finite volume Hermite weighted essential non-oscillatory （HWENO） methods to solve hyperbolic conservation laws. The key feature of the multi-step temporal discretization procedure is to use variable time step with strong stability preserving （SSP）. The multi-step tem- poral discretization methods can make full use of computed information with HWENO spatial discretization by holding the former computational values. Extensive numerical experiments are presented to demonstrate that the finite volume HWENO schemes with multi-step diseretization can achieve high order accuracy and maintain non-oscillatory properties near discontinuous region of the solution.
