Robust Schemes Based on the Method of Lines for Shock Capturing

Abstract

Abstract In this paper, the solution of nonlinear hyperbolic conservation law problems containing strong shock waves is presented using the method of lines. A difficulty with the method of lines, as with many other classical shock-capturing methods, is the threat of unphysical numerical oscillations, which can be avoided by adding an artificial viscosity term. Two schemes of the method of lines for solving the described problems have been proposed. Extensive numerical examples in both scalar and system test problems demonstrate the efficiency, robustness, and ease of implementation of the proposed schemes.