Implicit weighted ENO schemes for the three-dimensional incompressible Navier-Stokes equations

A class of lower-upper approximate-factorization implicit weighted essentially nonoscillatory (ENO) schemes for solving the three-dimensional incompressible Navier-Stokes equations in a generalized coordinate system is presented. The algorithm is based on the artificial compressibility formulation, and symmetric Gauss-Seidel relaxation is used for computing steady-state solutions. Weighted essentially nonoscillatory spatial operators are employed for inviscid fluxes and fourth-order central differencing for viscous fluxes. Two viscous flow test problems, laminar entry flow through a 90 degrees bent square duct and three-dimensional driven square cavity Bow, are presented to verify the numerical schemes. The use of the weighted ENO spatial operator not only enhances the accuracy of solutions but also improves the convergence rate for steady-state computation as compared with that using the ENO counterpart. It is found that the present solutions compare well with experimental data and other numerical results. (C) 1998 Academic Press.