应用TVD格式分离求解不可压N-S流动

提出一种新的将连续方程与动量方程分离求解的ＴＶＤ引用方法。对动量方程中的对流项采用三阶精度、迎风ＴＶＤ格式离散，粘性项和压力项采用中心差分格式离散。压力采用压力替代法求解。计算所用的网格是具有交错网格主要特点的修正非交错网格，并采用一种压力修正法和Ｇ－Ｓ中心对称迭代法加速收敛。给出了二维管流和二维空穴流动在不同状态下的计算结果，并与其它解法的计算结果或精确解进行比较。结果表明，ＴＶＤ格式不仅能用于不可压流数值计算，而且还能得到比非ＴＶＤ差分法精度更高的结果。

A METHOD OF USING TVD SCHEME TO CALCULATE INCOMPRESSIBLE FLOWS SEPARATELY

Abstract The Total Variation Diminishing (TVD) schemes have been adapted to incompressible flow computations.Considering the characters of the computation in the incompressible flow,a new method is given that the TVD sheme is used with separating the continue equation from momentum equations.The continuum governing equations are discretized on a modified nonstaggered grid.In the momentum equations,the convective terms are discretized by a third order TVD scheme,and the others are done by central finite difference scheme.The pressures are solved by pressure substitiution.Furthermore,a pressure correction procedure and the Gauss-Seidel centrally symmetric iteration algorithm are used to enhance the convergence rate.As a result,the code containing those methods has been applied to computation of two typical flow problems:the channel flow problem and the lid driven cavity flow problem.A comparison of the present results with the literature data is also given in good agreement.It is shown that the TVD scheme is not only applicable to incomprssible flow computation,but also it yields higher accuracy than the non TVD scheme.