Two-Phase Computational Model for Small-Amplitude Wave Propagation in a Saturated Porous Medium

Romenski, Evgeniy; Reshetova, Galina; Peshkov, Ilya; Dumbser, Michael

doi:10.1007/978-3-030-38870-6_41

Cited by 2 publications

(1 citation statement)

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“…It constitutes a monolithic mathematical framework that encompasses the evolution of all considered materials and provides a unified mathematical description of multi-physics systems, see e.g. [33] for a generalization of the two-phase flow model given in [34,36] to an arbitrary number of phases, [13,30] for applications of the SHTC theory to fluid and solid mechanics modeling, or [35] for recent advances in the description of poroelastic fluid-saturated media.…”

Section: Introductionmentioning

confidence: 99%

An all Mach number finite volume method for isentropic two-phase flow

Lukáčová-Medviďová¹,

Puppo²,

Thomann³

2022

Preprint

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We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the scheme consists of a linearisation of pressure and enthalpy terms at a reference state. The resulting stiff linear parts are integrated implicitly, whereas the non-linear higher order and transport terms are treated explicitly. Due to the flux splitting, the scheme is stable under a CFL condition which determined by the resolution of the slow material waves and allows large time steps even in the presence of fast acoustic waves. Further the singular Mach number limits of the model are studied and the asymptotic preserving property of the scheme is proven. In numerical simulations the consistency with single phase flow, accuracy and the approximation of material waves in different Mach number regimes are assessed.

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