The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

A Godunov-type method for the seven-equation model of compressible two-phase flow

“…The discretization technique of [37] is improved by the same authors in [38]. Then, in Andrianov & Warnecke [5] and Schwendeman, Wahle & Kapila [40], the common objective is to get exact solutions for the Riemann problem of the model. The approach is inverse in [5] in the sense that the initial left and right states are obtained as function of the intermediate states of the solution.…”

“…The approach is inverse in [5] in the sense that the initial left and right states are obtained as function of the intermediate states of the solution. On the contrary, a direct iterative approach is used in [40] leading to exact solutions of the Riemann problem for any initial left and right states. See also the recent work of Deledicque & Papalexandris [15].…”

“…In this work the authors propose to solve the Riemann problem approximately assuming that all the nonlinear characteristic fields are associated with rarefaction waves. More recently, Tokareva & Toro propose in [42] a HLLC-type approximate Riemann solver which takes into account all the seven waves that are naturally present in the model, and that can be seen as a similar but faster approach in comparison to the exact solver proposed in [40]. Finally, all these (approximate or exact) solutions are used to develop a Godunov-type method.…”

Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows

“…It was first proposed in Baer & Nunziato [4] and has since aroused more and more interest, see for instance Embid & Baer [7], Stewart & Wendroff [13], Abgrall & Saurel [11], Gallouët, Hérard & Seguin [8], Andrianov & Warnecke [3], Karni et al [9] Schwendeman, Wahle & Kapila [12], Munkejord [10], Tokareva & Toro [14], Ambroso, Chalons, Coquel & Galié [1], Ambroso, Chalons & Raviart [2], and the references therein. One of the main features of this model is that it is hyperbolic, at least in the context of subsonic flows.…”

“…This property will be used in the numerical strategy. Numerous papers are devoted to the numerical study of two-fluid two-pressure models, see again for instance [8], [3], [9], [12], [10], [14], [1], [2] and the references therein. Many of the proposed methods are based on time-explicit, exact or approximate, Godunov-type methods (Roe or Roe-like scheme, HLL or HLLC scheme...).…”