Second- and Third-Order Noncentered Difference Schemes for Nonlinear Hyperbolic Equations

Abstract

Second- and third-order, explicit finite-difference schemes are described for the numerical solution of the hyperbolic equations of fluid dynamics. The schemes are uncentered in the sense that spatial derivatives are generally approximated by forward or backward difference quotients. The advantages of noncentered methods over the more conventional centered schemes are: programing logic is simpler, nonhomogeneous terms are easily included, and generalization to multidimensional problems is direct. The von Neumann stability analysis for the proposed methods is reviewed and second- and third-order methods are compared with regard to dissipative and dispersive errors and shock-capturing ability.