三维非定常不可压涡量—速度Navier-Stokes方程组的有限差分法

FINITE DIFFERENCE METHOD FOR SOLVING THE 3D UNSTEADY INCOMPRESSIBLE VORTICITY-VELOCITY NAVIER-STOKES EQUATIONS

提出了一种数值求解三维非定常涡量一速度形式的不可压Navier-Stokes方程组的有限差分方法,该方法在空间方向上具有二阶精度,并且系数矩阵具有对角占优性,因此适合高雷诺数问题的数值求解.同时,给出了适合的二阶涡量边界条件.通过对有精确解的狄利克雷边值问题和典型的驱动方腔流问题的数值实验,验证了本文格式的精确性、稳定性和有效性.

A finite difference method is proposed for solving the 3D unsteady incompressible Navier- Stokes equations in vorticity-velocity formulation. The scheme is first-order accurate in time and second-order accurate in space. Because the coefficient matrix is diagonally dominant, it suits the solution of high Reynolds number problems. At the same time, a suitable second-order accurate discretization for vorticity boundary condition is presented accordingly. Lastly, an exact solution problem and the driven flow in a cubic cavity problem are employed to verify the accuracy, stability and effectiveness of the present method.