高黏性流动有限元模拟的迭代稳定分步算法

分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于某个临界值方能使算法稳定. 然而在高黏性流动模拟中，已有的显式和半隐式分步算法由于其显式本质，必须采用小时间步长计算，不但降低了计算效率，同时也常与为使分步算法稳分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于某个临界值方能使算法稳定. 然而在高黏性流动模拟中，已有的显式和半隐式分步算法由于其显式本质，必须采用小时间步长计算，不但降低了计算效率，同时也常与为使分步算法稳定必须满足的最小时间步长要求冲突. 本文目的是构造一种含迭代格式的分步算法，它能在保证精度的前提下大幅度地增大时间步长. 方腔流和平面Poisseuille流数值计算结果证实了此特点，该方法被有效应用于充填流动过程的数值模拟.

An iterative stabilized fractional step algorithm for finite element analysis in high-viscosity fluid flows

Stabilized fractional step algorithm has been widely accepted for numerical solution of the incompressible N-S equations. Based on Guermond's works, the stability of the fractional step algorithm requires that the time step size should be larger than a critical value. However, in modeling of high-viscosity fluid flows, existing explicit and semi-implicit versions of the algorithm require to use smaller time step sizes due to their explicit nature, which reduces the efficiency of the numerical solution procedure and very often conflicts with the minimum time step size requirement presented to ensure the stability of the fractional step algorithm. The purpose of this paper is to present a modified version of the fractional step algorithm, which allows much larger time step sizes than those for the preceding ones. The method is based on introducing an iteration algorithm. Numerical experiments in the cavity flow and the plane Poisseuille flow problems demonstrate the improved performance of the proposed modified version of the fractional step algorithm, which is further successfully applied to numerical simulation of the polymer injection molding process with high efficiency.