A conservative approximation to compressible two-phase flow models in the stiff mechanical relaxation limit

Wave Propagation in Multicomponent Flow Models

“…Here the energy equations were neglected. Several authors [9,12,16,21,22] have performed analytical and numerical studies of the full relaxation process where both µ p → ∞ and µ v → ∞, which results in a five-equation simplified system also briefly described by Stewart and Wendroff [24]. This system may be written in the following form [16]:…”

“…We emphasize that since the system is partially non-conservative, there is no obvious preferred choice of variables in which to express the balance equations; however, conservation of total energy must be respected. For the (N = 2)-model previously investigated, the authors [9,12,16,21,22] commonly choose to express the equations in terms of total energy and volume fraction, as stated by (20)- (24). This formulation naturally follows from performing the relaxation procedure on the model (12)-(18).…”

“…In this section, we wish to illustrate that our model essentially reduces to the five-equation model [9,12,16,21,22] for the special case N = 2. From our general model (76)-(78), we may derive an evolution equation for the volume fraction:…”

A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver

“…Since the late 80s, a variety of Riemann solvers and numerical methods have been developed for compressible two-phase flow, starting from the work reported in [24], in 1989. See also [8][9][10][11][12][13][14][15][16]. In 1997 Tiselj and Petelin [13] proposed a six equation model for twophase flow from the computer code RELAP5.…”

The Godunov Method for Calculating Multidimensional Flows of a One-Velocity Multicomponent Mixture

“…One-velocity models of multicomponent media are used in simulating wave processes in foamy liquids, polymers, and bubble liquids, for localization of contact surfaces in multifl uid hydrodynamics, in developing cavitation models, and in calculating detonation phenomena. In addition to the generalized-equilibrium model (GEM) of an n-component medium [1] used in the present work, in the literature there are other hyperbolic models describing fl ows of binary mixtures [2][3][4][5][6], not all of which, in contrast to the GEM, are reducible to a divergent form. It is known that when equations are used in a divergent form, the fi nite-volume schemes are conservative; therefore calculations by such schemes allow one to accurately follow both the positions and amplitudes of shock jumps [7].…”