Abstract
The second author of this paper has designed a conservative front-tracking method. The method tracks discontinuities by using the conservation property of the hyperbolic conservation laws rather than the Hugoniot condition. We compute the numerical solution on each side of a discontinuity using information only from the same side. In this paper, we develop the method for one-dimensional scalar conservation laws with nonconvex flux. Numerical examples are presented to show the robustness and accuracy of the method.
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Hu, J., Mao, D. (2012). A Conservative Front-Tracking Method for Scalar Conservation Laws in One Space Dimension with Nonconvex Flux. In: Xiao, T., Zhang, L., Ma, S. (eds) System Simulation and Scientific Computing. ICSC 2012. Communications in Computer and Information Science, vol 327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34396-4_10
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DOI: https://doi.org/10.1007/978-3-642-34396-4_10
Publisher Name: Springer, Berlin, Heidelberg
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