Conservative Front Tracking with Improved Accuracy

Abstract

We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has ${\mathcal O}(\Delta x)$ errors, improving over ${\mathcal O}(1)$ errors commonly found near a discontinuity. Numerical experiments which confirm these assertions are presented.