Roe Linearization for the van der Waals Gas

An extension of the Roe linearization method to nonideal gases is described and applied to the particular case of the van der Waals gas. A supplementary relation connecting the thermodynamic variables is introduced to decouple the evaluation of the intermediate velocity and total specific enthalpy from the determination of the intermediate density, needed in the Jacobian matrix of the linearization due to the 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 the 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.