在正常网格下解Navier-Stokes方程的有限分析法

Finite Analytic Numerical Solution of Navier-Stokes Equations with Regular Grid

以往在用有限分析法来解Navier-Stokes方程时,速度从动量方程解出,采用有限分析法,压力从连续方程解出,实际上采用了差分法。因此不得不使用交叉网格处理。这使收敛速度较慢,并降低了计算精度。本文提出一种新的处理连续方程的方式,使压力可由有限分析法解出,并且采用正常网格。计算实践表明,这种处理方式提高了计算精度,加快了收敛速度。

The Finite Analytic Method is an efficient numerical method to solve the Navier-Stokes equations. In the previous works the velocity is solved from the momentum equation by Finite Analytic Method and the pressure is solved from the continuity equation by Finite Difference Method, in which the pressure linked equation has a ship form so that the staggered grid scheme has to be used. However, the staggered grid is inconvenient and less accurate. This paper presents a new pressure linked equation, in which the skip form is avoided. Consequently, the regular grid can be employed again and the pressure can also be solved by Finite Analytic Method.