A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of ...A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.展开更多
The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the ...The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.展开更多
Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmos...Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.展开更多
September 12,2001 we propose a fully conservative front tracking algorithm in two space dimension. This algorithm first uses the point shifted algorithm on two adjacent time levels and then constructs space time hexah...September 12,2001 we propose a fully conservative front tracking algorithm in two space dimension. This algorithm first uses the point shifted algorithm on two adjacent time levels and then constructs space time hexahedra as computational units. We develop and prove a successful geometric construction under certain interface requirement. The algorithm has a first order local truncation error for cells near the tracked discontinuity, which is an improvement by one order of accuracy over most finite difference schemes, which have O (1) local truncation errors near discontinuities.展开更多
In this paper, a numerical method is given to solve relativistic hydrodynamic equations with source terms by conservative finite difference scheme. In calculation, QGP (quark gluon plasma) phase transition is als...In this paper, a numerical method is given to solve relativistic hydrodynamic equations with source terms by conservative finite difference scheme. In calculation, QGP (quark gluon plasma) phase transition is also considered. The numerical experiments have verified the effectiveness of the numerical method and some computational results are illustrated.展开更多
A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is pr...A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is proved in order O(h(2) + r(2)). In the proof, a new skill is used to deal with the term of difference quotient (e(j,k)(n))t. This is necessary, since there is no estimate of E(x, y, t) in L-infinity norm.展开更多
In this paper, a new conservative finite difference scheme with a parameter θ is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov （KGZ） equations. Convergence of the numerical solutions are pr...In this paper, a new conservative finite difference scheme with a parameter θ is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov （KGZ） equations. Convergence of the numerical solutions are proved with order O（h^2 ＋τ^2） in the energy norm. Numerical results show that the scheme is accurate and efficient.展开更多
In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be...In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.展开更多
基金The Project Supported by National Natural Science Foundation of China.
文摘A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.
文摘The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.
基金the Outstanding State Key Laboratory Project of National Science Foundation of China (Grant No. 40023001 )the Key Innovatio
文摘Based on the forced dissipetive nonlinear evolution equations for describing the motion of atmosphere and ocean, the computational stability of the explicit difference schemes of the forced dissipotive nonlinear atmospheric and oceanic equations is analyzed and the computationally stable explicit complete square conservative difference schemes are constructed. The theoretical analysis and numerical experiment prove that the explicit complete square conservative difference schemes are computationally stable and deserve to be disseminated.
基金the MICS program of the U.S.Department of Energy DE-FG0 2 -90 ER2 5 0 84the Departm ent of Energy ContractDE-AC0 2 -98CH1-886and the Office of Inertial Fusion+2 种基金the Army Research OfficeGrant DAAD19-0 1-1-0 64 2 the National ScienceFoun
文摘September 12,2001 we propose a fully conservative front tracking algorithm in two space dimension. This algorithm first uses the point shifted algorithm on two adjacent time levels and then constructs space time hexahedra as computational units. We develop and prove a successful geometric construction under certain interface requirement. The algorithm has a first order local truncation error for cells near the tracked discontinuity, which is an improvement by one order of accuracy over most finite difference schemes, which have O (1) local truncation errors near discontinuities.
文摘In this paper, a numerical method is given to solve relativistic hydrodynamic equations with source terms by conservative finite difference scheme. In calculation, QGP (quark gluon plasma) phase transition is also considered. The numerical experiments have verified the effectiveness of the numerical method and some computational results are illustrated.
文摘A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is proved in order O(h(2) + r(2)). In the proof, a new skill is used to deal with the term of difference quotient (e(j,k)(n))t. This is necessary, since there is no estimate of E(x, y, t) in L-infinity norm.
基金Supported by the National Natural Science Foundation of China (No. 10471023,11001034.)
文摘In this paper, a new conservative finite difference scheme with a parameter θ is proposed for the initial-boundary problem of the Klein-Gordon-Zakharov （KGZ） equations. Convergence of the numerical solutions are proved with order O（h^2 ＋τ^2） in the energy norm. Numerical results show that the scheme is accurate and efficient.
基金This research was supported by RSCF project No 14-17-00219.The authors would like to thank Prof.Emmanuel AUDUSSE(UniversitéParis 13,France)who brought our attention to the problem of boundary conditions for the SGN equations.
文摘In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.
