General solution procedure for flows in local chemical equilibrium

A comparison of hyperbolic solvers for ideal and real gas flows

“…A different approach based on finding a generalized Roe average state was taken by Grossman and Walters (1989), Glaister (1988), Liou et al (1990), Vinokur and Montagné (1990), Abgrall (1991), Toumi (1992), Cox and Cinnella (1994) and Mottura et al (1997). This average state includes the thermodynamics derivatives as additional variables and is responsible for the uniqueness of the average state.…”

Numerical simulations of mixtures of fluids using upwind algorithms

“…The compressibility factor for the mixture has to be a mole-averaged value (question 1 in Section 3), the mixture rule does reduce to Agamat's Law when only liquids are present (question 2 in Section 3), and Eqs. (11) and (14) are indeed mass-averaging rules (question 3 in Section 3).…”

“…(10), (11), and (14) can be further analyzed and evaluated in light of the three questions that were posed at the beginning of Section 3. In the following, the hypothesis of Ideal Solutions shall be utilized, allowing one to determine the partial specific volumes ðvÞ Ã i from the mixture pressure and temperature.…”

Roe Linearization for the van der Waals Gas

“…To extend Roe solver to gas models different from the ideal polytropic one, several approaches have been followed [1,7,10,12,19,33]. It has been noticed [23] that all these methods can be written so as to obtain a quasi-Jacobian form for the Roe matrix, in which the original intermediate state (ũ, h t ) of Roe is augmented by additional unknowns, namely, the pressure derivatives (either with respect to the conservative variables or with respect to two independent thermodynamic variables).…”

“…Most of the formulations of Roe's method developed to deal with a general equation of state [1,7,10,12,19,33] may be described as linearizations in quasi-Jacobian form [23], where the thermodynamic pressure derivatives are considered as additional unknowns that provide sufficient degrees of freedom to make the solution of the linearization problem unique. The proposed method follows a different approach, in which a strictly Jacobian form is retained-thus ensuring the hyperbolic character of the linearized problem-while the density is raised to the role of the required additional unknown.…”