The unresolved transition array(UTA) simulation with configuration average approximation is used to calculate the spectral properties of plasmas involving complex ions.This method is used to simulate the transmission ...The unresolved transition array(UTA) simulation with configuration average approximation is used to calculate the spectral properties of plasmas involving complex ions.This method is used to simulate the transmission of X-rays through aluminum plasma and niobium plasma respectively.The results are compared with experiments and other results of advanced models and good agreements are obtained.展开更多
The Boussinesq approximation ,where the viscosity depends polynomially on the shear rate ,finds more and more frequent use in geological practice,In this paper ,we consider the periodic initial value problem and inita...The Boussinesq approximation ,where the viscosity depends polynomially on the shear rate ,finds more and more frequent use in geological practice,In this paper ,we consider the periodic initial value problem and inital value problem for this modified Boussinesq approximation with the viscous part of the stress tensor T^v=τ(e)-μ1△e,where the nonlinear function τ(e) satisfies τij(e)eij≥C|e|^p or τij(e)eij ≥C(|e|^2+|e|^p).The existence,uniqueness and regulartiy of the weak solution is proved for p> 2n/(n+2).展开更多
The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of...The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2^(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.展开更多
In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of R^d (d = 2 or 3) with Robin boundary condition. Upwinding approximations are...In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of R^d (d = 2 or 3) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and L^2 and H^1 spacial norm convergence properties are obtained.展开更多
In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spaces...In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spacestep and timestep.展开更多
In transport theory, the convergence of the inner iteration scheme to the spherical neutron transport equation has been an open problem. In this paper, the inner iteration for a positive step function scheme is consid...In transport theory, the convergence of the inner iteration scheme to the spherical neutron transport equation has been an open problem. In this paper, the inner iteration for a positive step function scheme is considered and its convergence in spherical geometry is proved.展开更多
基金Supported by Laboratory for Shock Wave and Detonation Physics Pesearch,Institute of Fluid Physics,and the by research grant No.970230 of the China Academy of Engineering Physics
文摘The unresolved transition array(UTA) simulation with configuration average approximation is used to calculate the spectral properties of plasmas involving complex ions.This method is used to simulate the transmission of X-rays through aluminum plasma and niobium plasma respectively.The results are compared with experiments and other results of advanced models and good agreements are obtained.
文摘The Boussinesq approximation ,where the viscosity depends polynomially on the shear rate ,finds more and more frequent use in geological practice,In this paper ,we consider the periodic initial value problem and inital value problem for this modified Boussinesq approximation with the viscous part of the stress tensor T^v=τ(e)-μ1△e,where the nonlinear function τ(e) satisfies τij(e)eij≥C|e|^p or τij(e)eij ≥C(|e|^2+|e|^p).The existence,uniqueness and regulartiy of the weak solution is proved for p> 2n/(n+2).
基金Project supported by China "National Key Program for Developing Basic Sciences" (No.G1999032801) the National Natural Science Foundation of China (No.19932010) the Science and Technology Foundation of Chinese Academy of Engineering Physics (No.200206
文摘The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2^(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.
文摘In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of R^d (d = 2 or 3) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and L^2 and H^1 spacial norm convergence properties are obtained.
文摘In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spacestep and timestep.
文摘In transport theory, the convergence of the inner iteration scheme to the spherical neutron transport equation has been an open problem. In this paper, the inner iteration for a positive step function scheme is considered and its convergence in spherical geometry is proved.
