Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

The compressible Navier-Stokes equations are solved in thin-layer form for a variety of two-dimension al inviscid and viscous problems by preconditione d conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. An approximate system of linear equations that arises out of the linearization of a fully implicit scheme is solved iteratively by the generalized minimum residual technique and Chebychev iteration. Incomplete lower-upper factorization and block diagonal factorization are tested as preconditioned. The resulting algorithm is found to be competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

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