On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes

Abstract

This paper presents a class of explicit and implicit second order accurate finite-difference schemes for the computation of weak solutions of hyperbolic conservation laws. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurate scheme to an appropriately modified flux. The so derived second order accurate schemes achieve high resolution, while retaining the robustness of the original first order accurate scheme.