不可压Navier-Stokes方程的隐式投影法

IMPLICIT PROJECTION METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

起的解的小尺度以外,还有解的约束条件,即(1.1)。为了分辨小尺度,需用足够小的网格;而为了保证计算效率,时间步△_t需适当地大,从而必须用隐式格式。但是,由于解的约束条件,隐式格式的实现有困难,为此可用所谓的投影法,如[1]-[3]。前两者基于全隐式或Crank-Nicholson(CN)隐式和所谓的全投影;后者基于CN和压力修正投影。当然可以同时迭代u,v,p而得出每时间层的解,如[4]中的Peyret以及[5]中的Spolding-

This paper presents a modified version of the completely implicit Teman scheme [1]with centered differencing on the staggered grid for numerical solution of the incompressibleNavier-Stokes equations, and proves that it retains the original unconditional nonlinear sta-bility. For large △t, implicit schemes with proiection methods have not met with expected su-ccess in practical computation. This paper analyzes two projection methods under simplifyingassumptions, the complete projection method and the pressure correction method, based oncompletely implicit schemes. The result shows, in particular, that the former converges (tosteady state) fast, but the steady-state solution is dependent on △t; the latter produces steady-state solution independent of △t, but the convergent process is slow for large △t. This workimproves the convergence of the pressure correction method under certain conditions, andgives relevant numerical results