Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows

Abstract

Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock I. Introduction 1T4 this paper we consider the application of explicit Isecond-order, one-sided or upwind, difference schemes for the numerical solution of hyperbolic systems in conservation-law form = 0