Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were de...Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from (0.3) to (0.8) and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.展开更多
提出了一种基于m次重启的简化广义最小残差法(simpler generalized minimal residual algorithm of m times restart,SGMRES(m))的电力系统暂态稳定仿真新算法,即采用SGMRES(m)方法对暂态稳定仿真中形成的线性方程组进行求解,通过修正...提出了一种基于m次重启的简化广义最小残差法(simpler generalized minimal residual algorithm of m times restart,SGMRES(m))的电力系统暂态稳定仿真新算法,即采用SGMRES(m)方法对暂态稳定仿真中形成的线性方程组进行求解,通过修正标准正交基的生成过程,使得m阶上Hessenberg矩阵成为上三角矩阵。这样,只要通过简单的上三角线性方程组的求解即可求得解的修正量,避免了求解广义最小残差法每次迭代中的最小二乘问题,从而有效地减少了计算量。为进一步加快计算速度,文中算法进一步结合了伪牛顿策略和不完全LU预处理技术。多个算例的计算结果表明,所提出方法是有效的。展开更多
文摘Based on the first-order upwind and second-order central type of finite volume (UFV and CFV) scheme, upwind and central type of perturbation finite volume (UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from (0.3) to (0.8) and convergence perform excellent with Reynolds number variation from 10~2 to 10~4.
文摘提出了一种基于m次重启的简化广义最小残差法(simpler generalized minimal residual algorithm of m times restart,SGMRES(m))的电力系统暂态稳定仿真新算法,即采用SGMRES(m)方法对暂态稳定仿真中形成的线性方程组进行求解,通过修正标准正交基的生成过程,使得m阶上Hessenberg矩阵成为上三角矩阵。这样,只要通过简单的上三角线性方程组的求解即可求得解的修正量,避免了求解广义最小残差法每次迭代中的最小二乘问题,从而有效地减少了计算量。为进一步加快计算速度,文中算法进一步结合了伪牛顿策略和不完全LU预处理技术。多个算例的计算结果表明,所提出方法是有效的。
