Application of two-point implicit central-difference methods to hyperbolic systems

Abstract

This paper presents a general solution algorithm for the set of difference equations that arise when two-point 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.