Second order scheme for scalar conservation laws with discontinuous flux |
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| Affiliation: | 1. Department of Computational and Applied Mathematics, China University of Petroleum, Qingdao 266580, PR China;2. Department of Mathematics, East China Normal University, Shanghai 200062, PR China;3. Laboratório Nacional de Computação Científica, MCTI Avenida Getúlio Vargas 333, 25651-075 Petrópolis, RJ, Brazil;1. School of Science, Northwestern Polytechnical University, Xi''an, Shaanxi 710072, PR China;2. College of Science, Chang''an University, Xi''an, Shaanxi 710064, PR China;1. ITESRC, México;2. University of Catania, Italy;3. Universidad de Málaga, Spain;4. Universidad de Concepción, Chile;5. Universidad Internacional de Valencia, Spain;1. DISIM, University of L''Aquila, L''Aquila, Italy;2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea;3. Korea Institute for Advanced Study, Hoegiro 87, Seoul, 130-722, Republic of Korea;4. Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea |
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| Abstract: | Burger, Karlsen, Torres and Towers in [9] proposed a flux TVD (FTVD) second order scheme with Engquist–Osher flux, by using a new nonlocal limiter algorithm for scalar conservation laws with discontinuous flux modeling clarifier thickener units. In this work we show that their idea can be used to construct FTVD second order scheme for general fluxes like Godunov, Engquist–Osher, Lax–Friedrich, … satisfying (A, B)-interface entropy condition for a scalar conservation law with discontinuous flux with proper modification at the interface. Also corresponding convergence analysis is shown. We show further from numerical experiments that solutions obtained from these schemes are comparable with the second order schemes obtained from the minimod limiter. |
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| Keywords: | Discontinuous flux Second order schemes Sweeping algorithm (A, B)-entropy condition Flux TVD property |
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