We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge–Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.
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Bryson, S., Levy, D. On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws. J Sci Comput 27, 163–175 (2006). https://doi.org/10.1007/s10915-005-9046-8
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DOI: https://doi.org/10.1007/s10915-005-9046-8