TVD fluxes for the high-order ADER schemes. (English) Zbl 1096.76029

Summary: We propose to use a TVD flux, instead of a first-order monotone flux, as the building block for designing very high-order methods; we implement the idea in the context of ADER schemes via a new flux expansion. Systematic assessment of the new schemes shows substantial gains in accuracy; these are particularly evident for problems involving long time evolution


76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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