# An acoustic-convective splitting-based approach for the Kapila two-phase flow model

## TL;DR

This paper introduces a novel acoustic-convective splitting scheme for the Kapila two-phase flow model, enabling efficient and accurate numerical simulations of two-phase flows with general equations of state.

## Contribution

It presents a new splitting-based numerical method that decouples acoustic and convective waves for the Kapila model, improving computational simplicity and flexibility.

## Key findings

- Accurately simulates two-phase shock tube problems
- Achieves results in good agreement with reference solutions
- Demonstrates effectiveness of the splitting approach

## Abstract

In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splitting approach. The results are in good agreement with reference results and exact solutions.