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The application of preconditioning in viscous flows. (English) Zbl 0768.76032
A time-derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows has been developed. The algorithm uses a preconditioning matrix that introduces well-conditioned eigenvalues while simultaneously avoiding nonphysical time reversals for viscous flows. The resulting algorithm also provides a mechanism for controlling the inviscid and viscous time step parameters at very diffusive flows, thereby ensuring rapid convergence for very viscous flows as well as for inviscid flows.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
65F35 Numerical computation of matrix norms, conditioning, scaling
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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