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NASA NTRS · 20260005262

Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Nguyen Ly·Christopher DeGrendele·Francois Cadieux·Michael Barad·Jared Duensing
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Abstract

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

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ESGESDMDARMDPressure-equilibrium PreservingMultiphaseNumerical AlgorithmsTTT

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Nguyen Ly, Christopher DeGrendele, Francois Cadieux, Michael Barad, Jared Duensing. Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation. https://ntrs.nasa.gov/citations/20260005262

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ARMD subjectESDMD subjectESG subjectMultiphase subjectNumerical Algorithms subjectPressure-equilibrium Preserving subject

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