基于投影法求解不可压缩流的高精度紧致格式

A Projection-based High-order Compact Scheme for Solving Incompressible Flows

本文建立了一种基于投影法的求解不可压缩Navier-Stokes(N-S)方程的高精度紧致差分格式。该方法时间上采用Kim和Moin二阶投影法离散,空间上采用高精度紧致格式离散,并提出了一种新的离散压力边界的紧致格式,同时对计算结果进行分析以验证该投影法的精度和格式稳定性。文中Taylor涡列数值计算结果表明,Kim和Moin投影法能使得压力场和速度场均达到时间二阶精度,且高精度紧致格式投影法也具有空间高阶精度。驱动方腔数值模拟结果显示,本文对N-S方程的离散格式具有很好的可靠性,适用于对复杂流体流动的小尺度问题的数值模拟和研究。

In this paper, based on the Kim and Moin projection technique, we develop a high-order compact difference method with spatial order 4 and temporal order 2 for the solution of the incom- pressible Navier-Stokes equations. In particular, we propose a new compact discretization formula for the Neumann boundary condition of pressure. Numerical experiments are performed to validate the accuracy and robustness of the presented scheme. The simulation results of the regularized driven cavity are in good agreement with the existing solutions in the literature.