On the Kconsistence property of difference schemes of gas dynamics. I  An analysis of firstorder schemes. II  An analysis of secondorder schemes
Abstract
It is shown that it is possible to introduce the Kconsistence notion directly for finite difference shockcapturing schemes approximating the Euler equation system for an inviscid, compressible gas. Methods for increasing the accuracy of the numerical solutions in the vicinity of a contact discontinuity are proposed and theoretically justified. These methods are applicable in the cases when the equation of state employed does not satisfy the socalled Kconsistence condition and when the finite difference secondorder schemes are used for gas dynamic computations in Eulerian variables. The construction of corresponding algorithms is accomplished for the LaxWendroff scheme and the MacCormack scheme. Theoretical conclusions are illustrated by computational examples.
 Publication:

Computers and Fluids
 Pub Date:
 1982
 Bibcode:
 1982CF.....10..181V
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Finite Difference Theory;
 Gas Dynamics;
 Inviscid Flow;
 Numerical Stability;
 Shock Discontinuity;
 Equations Of State;
 Error Analysis;
 Euler Equations Of Motion;
 Fluid Pressure;
 Spline Functions;
 Velocity Errors;
 Fluid Mechanics and Heat Transfer