Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been...Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.展开更多
A parallel algorithm is developed for the two-dimensional time-dependent convective dominant-diffusion problem. An explicit alternating direction (EAD) method, which is based on the second-order compact upwind finite ...A parallel algorithm is developed for the two-dimensional time-dependent convective dominant-diffusion problem. An explicit alternating direction (EAD) method, which is based on the second-order compact upwind finite difference scheme, is studied. The algorithm is tested on a linear and a nonlinear differential equation using a parallel computer. Some numerical results show that the method has high accuracy and is ideally suitable for massively parallel computers.展开更多
This paper presents a kind of new Crank-Nicolson difference scheme for one and two dimensional convection-diffusion equations. It also gives the alternating direction method for two-dimensional problems. Because the c...This paper presents a kind of new Crank-Nicolson difference scheme for one and two dimensional convection-diffusion equations. It also gives the alternating direction method for two-dimensional problems. Because the coefficient matrix formed by the scheme is always diagonally dominant, the scheme can be solved by general iteration method. In this paper, we prove that the new CN scheme for one dimensional problems is convergent with respect to discrete L^2 norm with orderO(△t^2+△th+h^2). We also prove that the new CN scheme for two dimensional problems is stable by discrete Fourier method. Finally, numerical examples show that the method in this paper is very effective for solving convection-diffusion equations.展开更多
文摘Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.
文摘A parallel algorithm is developed for the two-dimensional time-dependent convective dominant-diffusion problem. An explicit alternating direction (EAD) method, which is based on the second-order compact upwind finite difference scheme, is studied. The algorithm is tested on a linear and a nonlinear differential equation using a parallel computer. Some numerical results show that the method has high accuracy and is ideally suitable for massively parallel computers.
文摘This paper presents a kind of new Crank-Nicolson difference scheme for one and two dimensional convection-diffusion equations. It also gives the alternating direction method for two-dimensional problems. Because the coefficient matrix formed by the scheme is always diagonally dominant, the scheme can be solved by general iteration method. In this paper, we prove that the new CN scheme for one dimensional problems is convergent with respect to discrete L^2 norm with orderO(△t^2+△th+h^2). We also prove that the new CN scheme for two dimensional problems is stable by discrete Fourier method. Finally, numerical examples show that the method in this paper is very effective for solving convection-diffusion equations.
