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A comparative study of different sets of variables for solving compressible and incompressible flows. (English) Zbl 0957.76028

Summary: A globally conservative Galerkin/least-squares formulation which attains correct shock structure is developed for any choice of variables. Only the choice of entropy variables satisfies exactly the discrete Clausius-Duhem inequality without any dissipative mechanisms, whereas for the rest of the variables, artificial diffusion is required to guarantee entropy production. The limit of the formulation is well defined for entropy variables and the primitive variables \((p,u,T)\), leading to conservative incompressible formulations. The approach is stable for any continuous interpolations, both for compressible and incompressible flows. A comparative study of different variables is performed, indicating that entropy variables and the primitive variables \((p,u,T)\) possess the most attributes for practical problem solving.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76D05 Navier-Stokes equations for incompressible viscous fluids
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