In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing...In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing some canonical momenta. To simulate the problem efficiently, the CNLS-KdV equations are approximated by a high order compact method in space which preserves N semi-discrete multisymplectic conservation laws. We then discretize the semi-discrete system by using a symplectic midpoint scheme in time. Thus, a full-discrete multisymplectic scheme is obtained for the CNLS-KdV equations. The conservation laws of the full-discrete scheme are analyzed. Some numerical experiments are presented to further verify the convergence and conservation laws of the new scheme.展开更多
In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume(...In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume(main cell) into several sub-cells and the finite volume discretization is applied to each of the sub-cells. The averaged values on the sub-cells of current and face neighboring main cells are used to reconstruct the polynomial distributions of the dependent variables. This method can achieve arbitrarily high order of accuracy using a compact stencil. It is similar to the spectral volume method incorporating with PNPM technique but with fundamental differences. An elaborate utilization of these differences overcomes some shortcomings of the spectral volume method and results in a family of accurate and robust schemes for solving the hyperbolic conservation laws. In this paper, the basic formulation of the proposed method is presented. The Fourier analysis is performed to study the properties of the one-dimensional schemes. A WENO limiter based on the secondary reconstruction is constructed.展开更多
An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direct...An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direction,respectively.The scheme is energy-preserving,stable,and of sixth order in space and of second order in time.Numerical experiments verify the theoretical results.The dynamic behavior modeled by the coupled Gross-Pitaevskii equations is also numerically investigated.展开更多
基金This work is supported by the NNSFC （Nos. 11771213, 41504078, 11301234, 11271171）, the National Key Research and Development Project of China （No. 2016YFC0600310）, the Major Projects of Natural Sciences of University in Jiangsu Province of China （No. 15KJA110002） and the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Provincial Natural Science Foundation of Jiangxi （Nos. 20161ACB20006, 20142BCB23009, 20151BAB 201012）.
文摘In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing some canonical momenta. To simulate the problem efficiently, the CNLS-KdV equations are approximated by a high order compact method in space which preserves N semi-discrete multisymplectic conservation laws. We then discretize the semi-discrete system by using a symplectic midpoint scheme in time. Thus, a full-discrete multisymplectic scheme is obtained for the CNLS-KdV equations. The conservation laws of the full-discrete scheme are analyzed. Some numerical experiments are presented to further verify the convergence and conservation laws of the new scheme.
基金supported by the National Natural Science Foundation of China(Grant Nos.U1430235,and 11672160)
文摘In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume(main cell) into several sub-cells and the finite volume discretization is applied to each of the sub-cells. The averaged values on the sub-cells of current and face neighboring main cells are used to reconstruct the polynomial distributions of the dependent variables. This method can achieve arbitrarily high order of accuracy using a compact stencil. It is similar to the spectral volume method incorporating with PNPM technique but with fundamental differences. An elaborate utilization of these differences overcomes some shortcomings of the spectral volume method and results in a family of accurate and robust schemes for solving the hyperbolic conservation laws. In this paper, the basic formulation of the proposed method is presented. The Fourier analysis is performed to study the properties of the one-dimensional schemes. A WENO limiter based on the secondary reconstruction is constructed.
基金supported by the National Natural Science Foundation of China(Nos.11771213,and 11961036)the Natural Science Foundation of Jiangxi Province(Nos.20161ACB20006,20142BCB23009,and 20181BAB201008).
文摘An energy-preserving scheme is proposed for the coupled Gross-Pitaevskii equations.The scheme is constructed by high order compact method in the spatial direction and average vector field method in the temporal direction,respectively.The scheme is energy-preserving,stable,and of sixth order in space and of second order in time.Numerical experiments verify the theoretical results.The dynamic behavior modeled by the coupled Gross-Pitaevskii equations is also numerically investigated.
