Numerical analysis of a model of two phase compressible fluid flow

TL;DR

This paper develops and analyzes a numerical scheme for simulating two-phase compressible fluid flow, ensuring stability, consistency, and convergence through advanced mathematical techniques.

Contribution

It introduces a new numerical scheme for binary compressible fluids and proves its convergence using generalized weak solutions and weak-strong uniqueness.

Findings

The scheme is stable and consistent.

Convergence is rigorously established.

The method effectively models two-phase compressible flows.

Abstract

We consider a model of a binary mixture of two immiscible compressible fluids. We propose a numerical scheme and discuss its basic properties: Stability, consistency, convergence. The convergence is established via the method of generalized weak solutions combined with the weak-strong uniqueness principle.