A Hierarchy of Relaxation Models for Two-Phase Flow
Halvor Lund
Source abstract
A hierarchy of relaxation two-phase flow models is considered, formulated as hyperbolic relaxation systems with source terms. The relaxation terms cause volume, heat, and mass transfer due to differences in pressure, temperature, and chemical potential, respectively, between the two phases. The subcharacteristic condition is a concept closely related to the stability of such relaxation systems. It states that the wave speeds of an equilibrium system never can exceed the speeds of the corresponding relaxation system. The work of Fl\aatten and Lund [Math. Models Methods Appl. Sci., 21 (2011), pp. 2379--2407] is extended, with analytical expressions for the wave velocities in each model in the mentioned hierarchy. The subcharacteristic condition is explicitly shown to be satisfied using sums of squares, subject only to physically fundamental assumptions.
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