# Convergence of the mac scheme for variable density flows

## TL;DR

This paper proves the convergence of a semi-implicit MAC scheme applied to the time-dependent variable density Navier-Stokes equations, ensuring numerical stability and accuracy for simulating variable density flows.

## Contribution

It provides a rigorous proof of convergence for the MAC scheme in the context of variable density flows, which was previously unestablished.

## Key findings

- Convergence of the scheme is mathematically established.
- The scheme is shown to be stable for variable density Navier-Stokes equations.
- The results support reliable numerical simulations of variable density flows.

## Abstract

We prove in this paper the convergence of an semi-implicit MAC scheme for the time-dependent variable density Navier-Stokes equations.