An implicit-explicit solver for a two-fluid single-temperature model

TL;DR

This paper introduces an implicit-explicit finite volume scheme for two-fluid single-temperature flows across all Mach regimes, emphasizing stability, efficiency, and asymptotic preservation.

Contribution

It develops a novel IMEX scheme based on symmetric hyperbolic thermodynamics, ensuring stability and efficiency for all Mach numbers in two-fluid models.

Findings

Scheme is stable for large time steps.

Achieves asymptotic preservation for weakly compressible flows.

Validated through multiple numerical tests.

Abstract

We present an implicit-explicit finite volume scheme for two-fluid single-temperature flow in all Mach number regimes which is based on a symmetric hyperbolic thermodynamically compatible description of the fluid flow. The scheme is stable for large time steps controlled by the interface transport and is computational efficient due to a linear implicit character. The latter is achieved by linearizing along constant reference states given by the asymptotic analysis of the single-temperature model. Thus, the use of a stiffly accurate IMEX Runge Kutta time integration and the centered treatment of pressure based quantities provably guarantee the asymptotic preserving property of the scheme for weakly compressible Euler equations with variable volume fraction. The properties of the first and second order scheme are validated by several numerical test cases.