解不可压缩流动N-S方程的隐式SMAC方法

该文基于SMAC(SimplifiedMarkerandCell)方法推导出了的一种直接求解不可压缩N-S方程的隐式数值方法。求解的基本方程是任意曲线坐标系下以逆变速度为变量的N-S方程和椭圆型的压力Poisson方程。压力Poisson方程用TschebyscheffSLOR方法交替方向迭代求解。N-S方程数值离散时对流项采用了Chakravaythy-OsherTVD格式。用该方法计算后台阶流场的结果与经典的实验结果相当吻合,表明该方法是可靠的,在合适的边界条件下求解不但是稳定的,而且能有效抑制流网扭曲大的地方产生较大的非物理振荡误差。

Implicit SMAC scheme for the incompressible Navier-Stokes equations

An implicit finite-difference method was developed based on the SMAC (simplified marker and cell) scheme for directly solving the incompressible N-S equations. The method solves the N-S equations based on the contravariant velocities and the elliptical Poisson pressure equation in general curvilinear coordinates. The pressure equation was solved using the Tschebyscheff SLOR method with alternating computational directions. The Chakravarthy-Osher TVD scheme was used to discretize the convective terms in the N-S equations. The consistency of computational results relative to the classic experimental results for the backward-facing step flow indicates that the present implicit scheme with the proper boundary conditions is not only stable, but can also efficiently suppress spurious errors even when the elements are seriously skewed.