IMPLICIT SOLVERS FOR UNSTRUCTURED MESHES

Implicit methods are developed and tested for unstructured mesh computations. The methods are used to solve the compressible Navier-Stokes equations to steady state. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (generalized minimum residual) technique. Three different preconditioners, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR) are investigated. The preconditioners have been optimized to have good vectorization properties. SSOR and ILU themselves are studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multi-element airfoil configurations using globally and adaptively generated meshes. © 1993 Academic Press, Inc.