非定常不可压缩Navier-Stokes方程的旋度形式压力校正格式分析

将求解不可压缩流动的旋度形式压力校正格式从Stokes方程延拓到非定常不可压缩Navier-Stokes方程.在第一步需要求解一个线性的对流-扩散方程,在第二步求解一个Stokes问题.首先给出格式的稳定性分析,然后采用P_2—P_1元分别使用标准形式的压力校正格式和旋度形式的压力校正格式进行了数值模拟,模拟结果表明,对于速度的L~2,H~1误差,两种格式几乎一样,对于压力的L~2误差,旋度形式的压力校正格式略有改进.

The Analysis of the Rotational Pressure-Correction Scheme for the Non-Stationary Navier-Stokes Equations

In this paper,the rotational pressure-correction scheme is extended from the Stokes equation to the non-stationary Navier-Stokes equations.In the first step,a linear advection-diffusion equation is solved,sequently,a Stokes equation is solved.Firstly,the stability of the scheme is presented,then a numerical example is given by virtue of the standard pressure-correction scheme and the rotational pressure-correction based on P_2— P_1element.The result shows that the rotational pressure-correction scheme does not improve the accuracy on the approximate velocity in the L~2,H~1-norm,However it does improve the accuracy on the approximate pressure in the L~2-norm slightly.