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Second order scheme for scalar conservation laws with discontinuous flux. (English) Zbl 1329.65177
Summary: Burger, Karlsen, Torres and Towers in [R. Bürger et al., Numer. Math. 116, No. 4, 579–617 (2010; Zbl 1204.65101)] 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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