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- W3080226205 abstract "The main result in this paper is a provably entropy stable shock capturing approach for the high order entropy stable Discontinuous Galerkin Spectral Element Method based on a hybrid blending with a subcell low order variant. Lead by theoretical findings presented in Fisher and Carpenter, where they show how to rewrite a high order summation-by-parts operator into an equivalent conservative finite difference form, it is possible to design a low order scheme directly with the Legendre-Gauss-Lobatto nodes that is compatible to the discrete entropy analysis used for the proof of the entropy stable DGSEM. We are able to design a hybrid low order/high order discretisation where it is possible to seamlessly blend between the two approaches, while still being provably entropy stable. With tensor products and careful design of the low order scheme on curved elements, we are able to extend the approach to three spatial dimensions on unstructured curvilinear hexahedral meshes. We validate our theoretical findings and demonstrate convergence order for smooth problems, conservation of the primary quantities and discrete entropy stability for an arbitrary blending on curvilinear grids. In practical simulations, we connect the blending factor to a local troubled element indicator that provides the control of the amount of low order dissipation injected into the high order scheme. We extended the shock indicator of Persson and Peraire to our provably stable hybrid scheme. We describe our indicator in detail and demonstrate its robustness in combination with the hybrid scheme, as it is possible to compute all the different test cases without changing the indicator. The test cases include e.g. the double Mach reflection setup, forward and backward facing steps with shock Mach numbers up to 100." @default.
- W3080226205 created "2020-09-01" @default.
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- W3080226205 date "2020-08-27" @default.
- W3080226205 modified "2023-09-27" @default.
- W3080226205 title "A provably entropy stable subcell shock capturing approach for high order split form DG" @default.
- W3080226205 hasPublicationYear "2020" @default.
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