非定常NS/Boussinesq方程的高精度多重网格方法

HIGH ACCURACY MULTIGRID SOLUTION FOR THE UNSTEADY NS/BOUSSINESQ EQUATIONS

提出了一种求解二维非定常不可压Navier—Stokes/Boussinesq方程的高精度全隐式紧致差分格式,为了提高隐格式的求解效率,在每一个时间步上,采用多重网格的全近似格式(FAS)加速其迭代收敛过程,其主要特点是既适于线性问题的求解又适用于非线性问题的求解。作为方法精确性和可靠性的验证,对方腔内部的自然对流问题进行了数值模拟。取Pr=0.71,在最大网格等分数为128×128网格上,Ra数最大算到107,所得结果与已有文献结果吻合的很好。

A compact fourth-order finite difference with a second-order fully implicit time-marching scheme is proposed to solve the unsteady Navier-Stokes/Bousinesq equations for two-dimensional, incompressible fluid flow and heat transfer using the vorticity-streamfunction formulation. A time-dependent multigrid full approximation storage(FAS) scheme, which is suitable for both linear and nonlinear problem, is employed to accelerate convergence for the implicit scheme at each time step. Numerical simulation of the natural convection in a square cavity is performed by the present method. The study demonstrates that the method developed here is very accurate, close agreement for all characteristic quantities with the data reported in literatures when Pr = 0.71 and the biggest Ra is 107 on 128×128 meshes.