This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it...This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it to magnetohydrodynamics(MHD)equations.The improved CESE method can improve the solution quality even with a large disparity in the Courant number(CFL)when using a fixed global marching time.Moreover,for a small CFL(say<0.1),the method can significantly reduce the numerical dissipation and retain the solution quality,which are verified by two benchmark problems.And meanwhile,comparison with the original CESE scheme shows better resolution of the improved scheme results.Finally,we demonstrate its validation through the application of this method in three-dimensional coronal dynamical structure with dipole magnetic fields and measured solar surface magnetic fields as the initial input.展开更多
In this paper,we construct a two-dimensional third-order space-time conservation element and solution element(CESE)method and apply it to the magnetohydrodynamics(MHD)equations.This third-order CESE method preserves a...In this paper,we construct a two-dimensional third-order space-time conservation element and solution element(CESE)method and apply it to the magnetohydrodynamics(MHD)equations.This third-order CESE method preserves all the favorable attributes of the original second-order CESEmethod,such as:(i)flux conservation in space and time without using an approximated Riemann solver,(ii)genuine multi-dimensional algorithm without dimensional splitting,(iii)the use of the most compact mesh stencil,involving only the immediate neighboring cells surrounding the cell where the solution at a new time step is sought,and(iv)an explicit,unified space-time integration procedure without using a quadrature integration procedure.In order to verify the accuracy and efficiency of the scheme,several 2D MHD test problems are presented.The result of MHD smooth wave problem shows third-order convergence of the scheme.The results of the other MHD test problems show that the method can enhance the solution quality by comparing with the original second-order CESE scheme.展开更多
基金supported by the National Basic Research Program of China(Grant No.2012CB825601)the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-01-4)+1 种基金the National Natural Science Foundation of China(Grant Nos.41031066,41231068,41074121&41074122)the Specialized Research Fund for State Key Laboratories
文摘This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it to magnetohydrodynamics(MHD)equations.The improved CESE method can improve the solution quality even with a large disparity in the Courant number(CFL)when using a fixed global marching time.Moreover,for a small CFL(say<0.1),the method can significantly reduce the numerical dissipation and retain the solution quality,which are verified by two benchmark problems.And meanwhile,comparison with the original CESE scheme shows better resolution of the improved scheme results.Finally,we demonstrate its validation through the application of this method in three-dimensional coronal dynamical structure with dipole magnetic fields and measured solar surface magnetic fields as the initial input.
基金supported by the National Natural Science Foundation of China(Grant Nos.42030204,41874202)Shenzhen Natural Science Fund(the Stable Support Plan Program GXWD20220817152453003)+1 种基金Shenzhen Key Laboratory Launching Project(No.ZDSYS20210702140800001)the Specialized Research Fund for State Key Laboratories.
文摘In this paper,we construct a two-dimensional third-order space-time conservation element and solution element(CESE)method and apply it to the magnetohydrodynamics(MHD)equations.This third-order CESE method preserves all the favorable attributes of the original second-order CESEmethod,such as:(i)flux conservation in space and time without using an approximated Riemann solver,(ii)genuine multi-dimensional algorithm without dimensional splitting,(iii)the use of the most compact mesh stencil,involving only the immediate neighboring cells surrounding the cell where the solution at a new time step is sought,and(iv)an explicit,unified space-time integration procedure without using a quadrature integration procedure.In order to verify the accuracy and efficiency of the scheme,several 2D MHD test problems are presented.The result of MHD smooth wave problem shows third-order convergence of the scheme.The results of the other MHD test problems show that the method can enhance the solution quality by comparing with the original second-order CESE scheme.
