A fourth-order compact finite difference scheme for the steady stream function-vorticity formulation of the Navier-Stokes/Boussinesq equations

作者：Tian ZF^*; Ge YB

来源：International Journal for Numerical Methods in Fluids, 2003, 41(5): 495-518.

DOI：10.1002/fld.444

• Navier-Stokes/Boussinesq equations
• stream-function-vorticity formulation
• compact scheme
• natural convection
• heated cavity problem

A fourth-order compact finite difference scheme on the nine-point 2D stencil is formulated for solving the steady-state Navier-Stokes/Boussinesq equations for two-dimensional, incompressible fluid flow and heat transfer using the stream function-vorticity formulation. The main feature of the new fourth-order compact scheme is that it allows point-successive overrelaxation (SOR) or point-successive under-relaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature.

• 出版日期2003-2-20
• 单位上海大学; 宁夏大学