## A unified approach for inviscid compressible and nearly incompressible flow by least-squares finite element method.(English)Zbl 1019.76024

Summary: We present a unified approach to treat inviscid compressible and incompressible flows. The formulation is based on the primitive variables $$W=(p,u,v)$$. In the case where the energy equation is present, we can either use the enthalpy $$h$$ or temperature $$T$$ in the primitive variables. The least-squares finite element method is applied in an unstructured framework. This method is well-defined for this set of variables, globally conservative and stable for any continuous interpolations, both for inviscid compressible and incompressible flows.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory) 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing

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