不同网格扭曲率下压力修正全隐算法——IDEAL求解性能研究

Performance study of pressure-correction fully-implicit algorithm—IDEAL on different grid skew rates

2008年,本文作者和陶文铨等提出了一种用于速度和压力耦合求解的高效稳定压力修正全隐算法IDEAL,该算法通过在每个迭代层次上对压力方程进行两次内迭代计算,完全克服了SIMPLE算法的两个假设,充分满足了速度和压力之间的耦合,从而大大提高了计算的收敛性和健壮性。为了进一步实现IDEAL算法的推广应用,本文基于三维倾斜方腔顶盖驱动流动,研究了IDEAL算法在不同网格扭曲率下的求解特性。研究发现,在不同网格扭曲率下,IDEAL算法的健壮性和收敛性均优于SIMPLE算法,特别在高网格扭曲率情况下,IDEAL算法求解性能更加优于SIMPLE算法。在不同网格扭曲率下,IDEAL算法健壮性保持不变,几乎可以在任意速度亚松弛因子下获得收敛的解,同时IDEAL算法最短计算耗时较SIMPLE算法减少了56%~89%,验证了IDEAL算法的优越性。

In 2008, an efficient pressure-correction fully-implicit algorithm for fluid flow and heat transfer problems, called IDEAL, was proposed by the present author and Tao et al. In IDEAL algorithm there exist inner double-iterative processes for pressure equation on each iteration level, almost completely overcoming two approximations in SIMPLE algorithm. Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence and robustness. In order to further extend the IDEAL algorithm, the lid-driven flow in a 3D inclined cavity is adopted to analyse its solving performance on different grid skew rates. It can be concluded that the IDEAL algorithm is more robust and more efficient than the SIMPLE algorithm on different grid skew rates, especially for the case of highly skewed grid system. The IDEAL algorithm keeps the same degree of robustness on different grid skew rates and can converge almost at any under-relaxation factor. Compared with the SIMPLE algorithm, the shortest computation time of the IDEAL algorithm can be reduced by 56%~89%. The superiority of the IDEAL algorithm is verified based on the above analyses.