Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations
Abstract
Although the NavierStokes equations describe most flows of interest in aerodynamics, the inviscid conservation law equations may be used for small regions with viscous forces. Thus, Euler equations and several timeaccurate finite difference procedures, explicit and implicit, are discussed. Although implicit techniques require more computational work, they permit larger time steps to be taken without instability. It is noted that the Jacobian matrices for Euler equations in conservationlaw form have certain eigenvalueeigenvector properties which may be used to construct conservativeform coefficient matrices. This reduces the computation time of several implicit and semiimplicit schemes. Extensions of the basic approach to other areas are suggested.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 February 1978
 DOI:
 10.1016/00457825(78)900567
 Bibcode:
 1978CMAME..13..175S
 Keywords:

 Conservation Equations;
 Euler Equations Of Motion;
 Finite Difference Theory;
 Computer Techniques;
 Conservation Laws;
 Eigenvalues;
 Eigenvectors;
 Inviscid Flow;
 Jacobi Matrix Method;
 NavierStokes Equation;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer