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Arbitrarily high-order accurate entropy stable essentially nonoscillatory schemes for systems of conservation laws. (English) Zbl 1252.65150
The paper deals with the numerical solution of conservation laws, namely the compressible Euler equations, with the aid of the finite volume technique. The authors develop the so-called TeCNO scheme, which represents a combination of ENO (essentially nonoscillatory) reconstruction and the entropy conservation. Such scheme is constructed and analysed, the third order of accuracy and the entropy stability are proven. Finally, several experiments using the TeCNO scheme up to 5th order are presented. The experiments indicate the accuracy and robustness of the numerical method.

MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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