Compact Finite Difference Schemes for the Euler and NavierStokes 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 entropyproducing scheme. An extension of the scheme also treats the compressible NavierStokes 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 March 1983
 DOI:
 10.1016/00219991(83)901389
 Bibcode:
 1983JCoPh..49..420R
 Keywords:

 Computational Fluid Dynamics;
 Conservation Laws;
 Euler Equations Of Motion;
 Finite Difference Theory;
 NavierStokes Equation;
 Perturbation Theory;
 Compressible Flow;
 Entropy;
 Hydrodynamics;
 Hyperbolic Differential Equations;
 Matrices (Mathematics);
 Fluid Mechanics and Heat Transfer