基于FIC法的不可压缩N-S方程稳定分步算法  

Stabilized fractional step algorithm for incompressible N-S equations based on FIC method

作　　者：陈善群[1] 廖斌[1] 

机构地区：[1]安徽工程大学建筑工程学院,安徽芜湖241000

出　　处：《水动力学研究与进展（A辑）》2015年第2期129-139,共11页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金项目(51175001);安徽省自然科学基金项目(1508085QE100);安徽高校省级科学研究项目基金(KJ2013B036)~~

摘　　要：近年来发展了一种稳定型分步算法,它是在有限增量微积分(Finite Increment Calculus,FIC)求解不可压缩N-S方程理论框架的基础上,引入了对流和压力梯度投影两个附加变量。该方法有效改善了经典分步算法的压力稳定性,同时避免了标准FIC理论框架中存在的空间高阶导数的计算。该文通过采用此方法对各种雷诺数条件下的顶盖驱动方腔流、圆柱绕流和后台阶流进行数值模拟,并将计算结果与前人计算结果及实验结果进行比较,结果表明本文算法计算结果合理可靠。由此可见该算法具有较强的求解不可压缩流动问题的能力以及良好的应用前景。On the basis of the theoretical framework of the Finite Increment Calculus （F1C） for solving incompressible N-S equations, a stabilized fractional step algorithm is developed by introducing two additional variables which are convection and pressure gradient projection. This method is effective in improving the classical fractional step algorithm for pressure stability, while avoiding the calculations of the high order spatial derivatives existed in the standard FIC procedure. Three example problems, i.e. the lid-driven cavity flow, flov~ around a cylinder and the backward facing step flow, are calculated and compared with the other calculation results and experimental data at different Reynolds numbers. The results show that the algorithm is reasonable and reliable, and the deviation of numerical solution occurs only under conditions of high Reynolds number. In summary, the algorithm has strong ability in solving incompressible flow and good application prospects.

关 键 词：FIC 分步算法 不可压缩N-S方程 方腔流 圆柱绕流 后台阶流 

分 类 号：TV131.2[水利工程—水力学及河流动力学]