We derive in this paper a time stable seventh-order dissipative compact finite difference scheme with simultaneous approximation terms(SATs) for solving two-dimensional Euler equations. To stabilize the scheme, the ch...We derive in this paper a time stable seventh-order dissipative compact finite difference scheme with simultaneous approximation terms(SATs) for solving two-dimensional Euler equations. To stabilize the scheme, the choice of penalty coefficients for SATs is studied in detail. It is demonstrated that the derived scheme is quite suitable for multi-block problems with different spacial steps. The implementation of the scheme for the case with curvilinear grids is also discussed.Numerical experiments show that the proposed scheme is stable and achieves the design seventh-order convergence rate.展开更多
We study the solution to the Fokker–Planck equation with piecewise-constant drift,taking the case with two jumps in the drift as an example.The solution in Laplace space can be expressed in closed analytic form,and i...We study the solution to the Fokker–Planck equation with piecewise-constant drift,taking the case with two jumps in the drift as an example.The solution in Laplace space can be expressed in closed analytic form,and its inverse can be obtained conveniently using some numerical inversion methods.The results obtained by numerical inversion can be regarded as exact solutions,enabling us to demonstrate the validity of some numerical methods for solving the Fokker–Planck equation.In particular,we use the solved problem as a benchmark example for demonstrating the fifth-order convergence rate of the finite difference scheme proposed previously[Chen Y and Deng X Phys.Rev.E 100(2019)053303].展开更多
The nonlinear Schr?dinger equation with a Dirac delta potential is considered in this paper.It is noted that the equation can be transformed into an equation with a drift-admitting jump.Then following the procedure pr...The nonlinear Schr?dinger equation with a Dirac delta potential is considered in this paper.It is noted that the equation can be transformed into an equation with a drift-admitting jump.Then following the procedure proposed in Chen and Deng(2018 Phys.Rev.E 98033302),a new second-order finite difference scheme is developed,which is justified by numerical examples.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11601517)the Basic Research Foundation of National University of Defense Technology(Grant No.ZDYYJ-CYJ20140101)
文摘We derive in this paper a time stable seventh-order dissipative compact finite difference scheme with simultaneous approximation terms(SATs) for solving two-dimensional Euler equations. To stabilize the scheme, the choice of penalty coefficients for SATs is studied in detail. It is demonstrated that the derived scheme is quite suitable for multi-block problems with different spacial steps. The implementation of the scheme for the case with curvilinear grids is also discussed.Numerical experiments show that the proposed scheme is stable and achieves the design seventh-order convergence rate.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11972370 and 61772542)。
文摘We study the solution to the Fokker–Planck equation with piecewise-constant drift,taking the case with two jumps in the drift as an example.The solution in Laplace space can be expressed in closed analytic form,and its inverse can be obtained conveniently using some numerical inversion methods.The results obtained by numerical inversion can be regarded as exact solutions,enabling us to demonstrate the validity of some numerical methods for solving the Fokker–Planck equation.In particular,we use the solved problem as a benchmark example for demonstrating the fifth-order convergence rate of the finite difference scheme proposed previously[Chen Y and Deng X Phys.Rev.E 100(2019)053303].
基金supported by the National Natural Science Foundation of China(Grant Nos.11601517,61772542).
文摘The nonlinear Schr?dinger equation with a Dirac delta potential is considered in this paper.It is noted that the equation can be transformed into an equation with a drift-admitting jump.Then following the procedure proposed in Chen and Deng(2018 Phys.Rev.E 98033302),a new second-order finite difference scheme is developed,which is justified by numerical examples.
