In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subal...In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.展开更多
In this paper, the Riemann problem with delta initial data for the onedimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics is considered. Under the generalized Rankine-Hug...In this paper, the Riemann problem with delta initial data for the onedimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics is considered. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtained the global existence of generalized solutions which contains delta-shock. Moreover, the author obtains the stability of generalized solutions by making use of the perturbation of the initial data.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
基金Supported by the National Natural Science Foundation of China under Grant No.11075055Innovative Research Team Program of the National Natural Science Foundation of China under Grant No.61021004Shanghai Leading Academic Discipline Project under Grant No.B412
文摘In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
基金supported by the TianY uan Special Funds of the National Natural Science Foundation of China(No.11226171)the Research Award Fund for Young Teachers in Shanghai Higher Education Institutions(No.shdj008)the Discipline Construction of Equipment Manufacturing System Optimization Calculation(No.13XKJC01)
文摘In this paper, the Riemann problem with delta initial data for the onedimensional system of conservation laws of mass, momentum and energy in zero-pressure gas dynamics is considered. Under the generalized Rankine-Hugoniot conditions and the entropy condition, we constructively obtained the global existence of generalized solutions which contains delta-shock. Moreover, the author obtains the stability of generalized solutions by making use of the perturbation of the initial data.
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.
