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WENO schemes based on upwind and centred TVD fluxes. (English) Zbl 1134.65361
Summary: We propose to use second-order TVD fluxes, instead of first-order monotone fluxes, in the framework of finite-volume weighted essentially non-oscillatory (WENO) schemes. We call the new improved schemes the WENO-TVD schemes. They include both upwind and centred schemes on non-staggered meshes. Numerical results suggest that our schemes are superior to the original schemes used with first-order monotone fluxes. This is especially so for long time evolution problems containing both smooth and non-smooth features.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
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