Implicit methods of second-order accuracy for the Euler equations. (English) Zbl 0556.76054

This paper presents a study of noniterative implicit finite difference methods for hyperbolic systems. New space-centered methods involving two time levels are considered. An analysis is made of various properties such as solvability, stability, dissipation, dispersion, and efficient solution of the algebraic systems. The computation of shock waves with a CFL number larger than the unity is discussed. Unconditional stability results are proved for a case having several space variables. Accurate solutions of the Euler equations are obtained that offer major reductions in computing costs over explicit methods.


76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics
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