Application of twopoint implicit centraldifference methods to hyperbolic systems
Abstract
This paper presents a general solution algorithm for the set of difference equations that arise when twopoint central differences are used to approximate the flux difference terms in systems of hyperbolic differential equations. The general algorithm eliminates the weak points associated with the nonstandard algorithm reported by Wornom and Hafez (1986). The disadvantages of their algorithm relate to its implementation. It consists of separate algorithms for subsonic, supersonic, sonic and shock cells, applied individually, which presents a major bookkeeping problem when multiple sonic and shock cells are present. The general algorithm eliminates this problem and introduces an improved shock treatment which produces shocks with at most one interior shock point.
 Publication:

Computers and Fluids
 Pub Date:
 1991
 Bibcode:
 1991CF.....20..321W
 Keywords:

 Euler Equations Of Motion;
 Hyperbolic Differential Equations;
 Inviscid Flow;
 One Dimensional Flow;
 Boundary Conditions;
 Computational Fluid Dynamics;
 Eigenvalues;
 Newton Methods;
 Nozzle Flow;
 Fluid Mechanics and Heat Transfer