Non-equilibrium Model for Weakly Compressible Multi-component Flows: the Hyperbolic Operator

TL;DR

This paper introduces a pressure-based, hyperbolic operator method for weakly compressible multiphase flows that avoids oscillations and CFL restrictions, validated through simplified test cases.

Contribution

It presents a novel hyperbolic operator for non-equilibrium multiphase flow modeling that handles non-conservative terms carefully to prevent spurious oscillations.

Findings

No spurious oscillations across interfaces

Good agreement with analytical solutions

Effective implicit treatment of acoustic equations

Abstract

We present a novel pressure-based method for weakly compressible multiphase flows, based on a non-equilibrium Baer and Nunziato-type model. In this work, we describe the hyperbolic operator, thus we do not consider relaxation terms. The acoustic part of the governing equations is treated implicitly to avoid the severe restriction on the time step imposed by the CFL condition at low-Mach. Particular care is taken to discretize the non-conservative terms to avoid spurious oscillations across multi-material interfaces. The absence of oscillations and the agreement with analytical or published solutions is demonstrated in simplified test cases, which confirm the validity of the proposed approach as a building block on which developing more accurate and comprehensive methods.