An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as compared to standard front tracking methods. The resulting algorithm is also more efficient than existing front tracking methods. The improved front tracking method is applied to the Euler equations for one-dimensional unsteady flow and two-dimensional steady supersonic flow. The results are compared to results of a standard front tracking method and a finite volume method.

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Journal of Computational Physics
Scientific Computing

Witteveen, J.A.S, Koren, B, & Bakker, P.G. (2007). An improved front tracking method for the Euler equations. Journal of Computational Physics, 224(2), 712–728.