Twophase compressible fluid dynamics with Cattaneo heat transfer*

The two-phase compressible fluid dynamics model introduced by Romenski etal. (2009, Journal of Scientific Computing) based on application of extended thermodynamics to continuum mixtures, provides a general and powerful mathematical formulation with many desirable properties. The arising system is conservative and entropy-generating. Moreover, given convex equation of states, the resulting system is hyperbolic, i.e., possessing real eigenvalues. Via relaxation source terms with appropriate time scale, this model also incorporate cavitation, both driven by expansion waves or local thermal irradiation. This work focuses on the single velocity and single temperature limit of this two-phase flow model applicable in very fast inter-phase thermal and momentum relaxation scenarios and considers finite-speed heat transfer modeling using Cattaneo heat conduction. Unlike the more common infinite speed heat condition of Fourier, the Cattaneo heat transfer is more suitable for small spatial scales heat conduction (of order of ~ 100 nm or smaller). The first eigenspectrum analysis of the system with the Cattaneo heat transfer is presented followed by a comparison with Fourier heat conduction.