Compact finite difference schemes for the Euler and Navier-Stokes equations

Abstract

Implicit compact finite difference schemes for the Euler equations are described which furnish equivalent treatment of the conservation and nonconservation forms; a simple modification yields an entropy-producing scheme. An extension of the scheme also treats the compressible Navier-Stokes equations; when the viscosity and heat conduction coefficients are negligible only the boundary data appropriate to the Euler equation influence the solution to any significant extent, a result consistent with singular perturbation theory.