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Numerical method for simulating rarefaction shocks in the approximation of phase-flip hydrodynamics

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Abstract

A finite-difference algorithm is proposed for numerical modeling of hydrodynamic flows with rarefaction shocks, in which the fluid undergoes a jump-like liquid-gas phase transition. This new type of flow discontinuity, unexplored so far in computational fluid dynamics, arises in the approximation of phase-flip (PF) hydrodynamics, where a highly dynamic fluid is allowed to reach the innermost limit of metastability at the spinodal, upon which an instantaneous relaxation to the full phase equilibrium (EQ) is assumed. A new element in the proposed method is artificial kinetics of the phase transition, represented by an artificial relaxation term in the energy equation for a “hidden” component of the internal energy, temporarily withdrawn from the fluid at the moment of the PF transition. When combined with an appropriate variant of artificial viscosity in the Lagrangian framework, the latter ensures convergence to exact discontinuous solutions, which is demonstrated with several test cases.

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  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, Moscow, 125047, Russia

    M. M. Basko

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Basko, M.M. Numerical method for simulating rarefaction shocks in the approximation of phase-flip hydrodynamics. Appl. Math. Mech.-Engl. Ed. 42, 871–884 (2021). https://doi.org/10.1007/s10483-021-2734-6

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  • DOI: https://doi.org/10.1007/s10483-021-2734-6

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