# Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

## TL;DR

This paper evaluates the accuracy of fully-coupled pressure-based algorithms without Riemann solvers in simulating shock-bubble interactions across different flow configurations, highlighting their effectiveness and limitations.

## Contribution

It demonstrates the predictive capabilities of pressure-based algorithms without Riemann solvers for shock-bubble interactions in gas-gas and liquid-gas flows, with insights on mesh resolution effects.

## Key findings

- Mesh resolution has minor influence in gas-gas flows.
- Mesh resolution critically affects liquid-gas bubble behavior.
- Pressure-based algorithms accurately model shock-bubble interactions.

## Abstract

The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based algorithms with pressure-correction methods as well as fully-coupled pressure-based algorithms have been established as promising alternatives to classical density-based algorithms based on Riemann solvers. The current paper investigates the predictive accuracy of fully-coupled pressure-based algorithms without Riemann solvers in modelling the interaction of shock waves with one-dimensional and two-dimensional bubbles in gas-gas and liquid-gas flows. For a gas bubble suspended in another gas, the mesh resolution and the applied advection schemes are found to only have a minor influence on the bubble shape and position, as well as the behaviour of the dominant shock waves and rarefaction fans. For a gas bubble suspended in a liquid, however, the mesh resolution has a critical influence on the shape, the position and the post-shock evolution of the bubble, as well as the pressure and temperature distribution.