Implicit weighted essentially non-oscillatory schemes for the incompressible Navier-Stokes equations

A class of lower-upper/approximate factorization (LUAF) implicit weighted essentially non-oscillatory (ENO; WENO) schemes for solving the two-dimensional incompressible Navier-Stokes equations in a generalized co-ordinate system is presented. The algorithm is based on the artificial compressibility formulation, and symmetric Gauss-Seidel relaxation is used for computing steady state solutions while symmetric successive overrelaxation is used for treating time-dependent flows. WENO spatial operators are employed for inviscid fluxes and central differencing for viscous fluxes. Internal and external viscous flow test problems are presented to verify the numerical schemes. The use of a WENO spatial operator not only enhances the accuracy of solutions but also improves the convergence rate for the steady state computation as compared with using the ENO counterpart. It is found that the present solutions compare well with exact solutions, experimental data and other numerical results. Copyright (C) 1999 John Wiley & Sons, Ltd.