Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly im...Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.展开更多
Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by ...Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.展开更多
A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative metho...A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of.the iteration.展开更多
A Newton/LU-SGS(lower-upper symmetric Gauss-Seidel)iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids.The Newton iteration...A Newton/LU-SGS(lower-upper symmetric Gauss-Seidel)iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids.The Newton iteration was employed to solve the nonlinear system,while the linear system was solved with LU-SGS iteration.The effect of several parameters in the implicit scheme,such as the CFL number,the Newton sub-iteration steps,and the update frequency of Jacobian matrix,was investigated to evaluate the performance of convergence history.Several typical test cases were simulated,and compared with the traditional explicit Runge-Kutta(RK)scheme.Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes.Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also.Finally,the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity.The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently.Choosing proper parameters would improve the efficiency of the implicit scheme.Moreover,in the same framework,the DG/FV hybrid schemes are more efficient than the same order DG schemes.展开更多
文摘Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.
文摘Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.
基金supported in part by NSF of China No.10571059E-Institutes of Shanghai Municipal Education Commission No.E03004+4 种基金Shanghai Priority Academic Discipline,and the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education MinistrySF of Shanghai No.04JC14062the fund of Chinese Education Ministry No.20040270002the Shanghai Leading Academic Discipline Project No.T0401the fund for E-Institutes of Shanghai Municipal Education Commission No.E03004 and the fund No.04DB15 of Shanghai Municipal Education Commission
文摘A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of.the iteration.
基金This work is supported partially by National Basic Research Program of China(Grant No.2009CB723800)by National Science Foundation of China(Grant Nos.11402290 and 91130029).
文摘A Newton/LU-SGS(lower-upper symmetric Gauss-Seidel)iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids.The Newton iteration was employed to solve the nonlinear system,while the linear system was solved with LU-SGS iteration.The effect of several parameters in the implicit scheme,such as the CFL number,the Newton sub-iteration steps,and the update frequency of Jacobian matrix,was investigated to evaluate the performance of convergence history.Several typical test cases were simulated,and compared with the traditional explicit Runge-Kutta(RK)scheme.Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes.Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also.Finally,the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity.The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently.Choosing proper parameters would improve the efficiency of the implicit scheme.Moreover,in the same framework,the DG/FV hybrid schemes are more efficient than the same order DG schemes.
