Numerical methods for interface coupling of compressible and almost incompressible media

TL;DR

This paper develops and implements advanced numerical methods for simulating shock wave interactions with complex interfaces between compressible gases and nearly incompressible solids or fluids, using high-resolution shock-capturing techniques and adaptive mesh refinement.

Contribution

It introduces new Riemann solvers and limiters for coupled Euler and Tammann equations, extending to mapped grids and AMR within the Clawpack framework.

Findings

Effective simulation of shock interactions with complex interfaces

Simplification of models when solid interfaces are very thin

Enhanced computational efficiency with AMR

Abstract

Many experiments in biomedical applications and other disciplines use a shock tube. These experiments often involve placing an experimental sample within a fluid-filled container, which is then placed inside the shock tube. The shock tube produces an initial shock that propagates through gas before hitting the container with the sample. In order to gain insight into the shock dynamics that is hard to obtain by experimental means, computational simulations of the shock wave passing from gas into a thin elastic solid and into a nearly incompressible fluid are developed. It is shown that if the solid interface is very thin, it can be neglected, simplifying the model. The model uses Euler equations for compressible fluids coupled with a Tammann equation of state (EOS) to model both compressible gas and almost incompressible materials. A three-dimensional (2D axisymmetric) model of these equations is solved using high-resolution shock-capturing methods, with newly developed Riemann solvers and limiters. The methods are extended to work on a mapped grid to allow more complicated interface geometry, and they are adapted to work with adaptive mesh refinement (AMR) for higher resolution and faster computations. The Clawpack software is used to implement the method. These methods were initially inspired by shock tube experiments to study the injury mechanisms of traumatic brain injury (TBI).