In this paper we investigate the performance of the weighted essential non-oscillatory （WENO） methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equ...In this paper we investigate the performance of the weighted essential non-oscillatory （WENO） methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the property, and resolution of discontinuities. issues of CPU cost, accuracy, non-oscillatory展开更多
In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory(WENO)schemes to solve the one-dimensional and two-dimensional shallow...In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory(WENO)schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms.Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values.Extensive simulations are performed,which indicate that,the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy,and are more cost effective than WENO scheme with Runge-Kutta time discretization,while still maintaining nonoscillatory properties.展开更多
基金supported by NSFC 40906048.The research of J.Qiu was supported by NSFC 10671091 and 10811120283support was provided by USA NSF DMS-0820348 while he was in residence at Department of Mathematical Sciences,Rensselaer Polytechnic Institutesupported by NSF of Hohai University 2048/408306
文摘In this paper we investigate the performance of the weighted essential non-oscillatory （WENO） methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the property, and resolution of discontinuities. issues of CPU cost, accuracy, non-oscillatory
基金supported by NSFC 40906048NSFC 41040042+1 种基金NSFC 40801200Science research fund of Nanjing University of information science&technology 20090203.
文摘In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory(WENO)schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms.Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values.Extensive simulations are performed,which indicate that,the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy,and are more cost effective than WENO scheme with Runge-Kutta time discretization,while still maintaining nonoscillatory properties.
