A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid

TL;DR

This paper introduces a relaxation-based coupling method for modeling the interaction between a two-phase vapor-liquid system and a linear-elastic solid, using advanced numerical schemes for improved simulation accuracy.

Contribution

It presents a novel coupling strategy employing Jin-Xin relaxation for two-phase fluids and elastic solids within a finite volume framework.

Findings

Successful one-dimensional simulations demonstrating the method's feasibility.

Effective coupling of hyperbolic systems with non-conservative products.

Potential for extending to more complex multi-dimensional problems.

Abstract

A recently developed coupling strategy for two nonconservative hyperbolic systems is employed to investigate a collapsing vapor bubble embedded in a liquid near a solid. For this purpose, an elastic solid modeled by a linear system of conservation laws is coupled to the two-phase Baer-Nunziato-type model for isothermal fluids, a nonlinear hyperbolic system with non-conservative products. For the coupling of the two systems the Jin-Xin relaxation concept is employed and embedded in a second order finite volume scheme. For a proof of concept simulations in one space dimension are performed.