Entropy Controlled Adaptive Finite Element Simulations for Compressible Gas Flow

The principal idea of the present work consists in using the entropy balance equation in its discrete form as a rationale for controling an optimal amount of artifficial dissipation in Finite Element (FE) compressible gas simulations. The entropy control can be reinterpreted as a nonlinear stability estimate in terms of the so-called modified entropy function. The idea has been practically verified using the Taylor-Galerkin method combined with an artificial viscosity term proposed by Hughes and Johnson, in context ofh-adaptive linear finite elements. The obtained numerical results confirm that the entropy control may indeed provide a basis for the careful balance between stability and higher-order resolution in FE approximations.

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