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Roe linearization for the van der Waals gas. (English) Zbl 1039.76038
Summary: An extension of Roe linearization method to nonideal gases is described and applied to the particular case of van der Waals gas. A supplementary relation connecting thermodynamic variables is introduced to decouple the evaluation of intermediate velocity and total specific enthalpy from the determination of intermediate density, needed in Jacobian matrix of the linearization due to general thermodynamic character of the gas. The density value is obtained by solving the supplementary equation, which involves the Roe average of velocity and enthalpy, and that in the case of polytropic van der Waals gas is a third-order algebraic equation. Numerical results are shown including classical and nonclassical behaviour in one-dimensional shock tube problems.

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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