基于5阶精度格式WCNS-E-5的p-multigrid方法研究

p-multigrid方法的基本思想是:在保证收敛结果为高阶精度的同时,利用低阶精度格式耗散大的特点,来改善高精度有限差分格式在迭代计算时收敛速度慢的弱点.本文基于5阶精度WCNS-E-5差分格式,引入1阶精度迎风格式和3阶精度加权格式,构造了p-multigrid方法,在迭代过程中采用了V循环、W循环、S循环、PreV和FMG循环等不同方式来应用这三种格式,并通过典型算例考察了这些循环方式对收敛速度的影响,初步数值试验表明,采用恰当的循环方式,本文所设计的p-multigrid方法能够加快收敛速度,并保证了最终收敛结果与5阶精度WCNS-E-5差分格式的一致性.

P-multigrid method based on the fifth order scheme WCNS-E-5

The basic principle of p-multigrid method is that it uses the low-order scheme’s high dissipation property to improve the weakness of low convergence rate,at the same time it guarantees the high-order accuracy of the solution.The p-multigrid method presented in this paper,is constructed by the fifth order finite differenc scheme——WCNS-E-5,the first order upwind scheme and the third order weighted scheme.During the iterative process the three different schemes are applied to construct the V-circle,W-circle,S-circle,Pre_V circle and FMG.The typical cases are calculated by the different circles to investigate the influence on the convergence rate.The primary numerical results indicate that when the appropriate circles are used,the p-multigrid method designed in this paper can accelerate the convergence rate,and at the same time guarantee the solution as the same as the fifth order finite difference scheme,WCNS-E-5.