同位网格上SIMPLE算法收敛特性的Fourier分析

Fourier analysis of the convergence behaviors of SIMPLE algorithm on collocated grid

应用Fourier方法研究了同位网格上SIMPLE算法求解浅水方程的收敛特性,并就松弛因子组合及阻力项的影响进行了分析。结果表明,采用合适的松弛因子组合可以很快地消除高频区域的误差,同时也可逐步消减迭代中低频区域的误差以获得收敛解。在保证收敛的前提下,低频误差分量决定了迭代速度,而且浅水方程中阻力项越大越利于SIMPLE算法收敛。

The Fourier analysis is employed to investigate the convergence behaviors of SIMPLE solver to shallow-water equations and check the effect of both relaxation factors and friction items on SIMPLE algorithm. The results indicate that appropriate combination of relaxation factors can damp out the high frequency effectively and keep the low frequency error reduced to convergence. In the case of convergence, the low frequency error dominates the rate of iteration and the growing influence of friction items makes for convergence.