The application of preconditioning in viscous flows. (English) Zbl 0768.76032

Choi, Y.-H.; Merkle, C. L.

J. Comput. Phys. 105, No. 2, 207-223 (1993).

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

Keywords:

time-derivative preconditioning algorithm; diffusive flows; preconditioning matrix; time step parameters; convergence