# Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows

## TL;DR

This paper analyzes how a pressure correction MAC scheme for compressible barotropic flows behaves as the Mach number approaches zero, showing convergence to an incompressible flow scheme under well-prepared initial data.

## Contribution

It proves the convergence of a pressure correction MAC scheme for compressible flows to the incompressible limit as Mach number tends to zero, under certain initial conditions.

## Key findings

- Numerical scheme converges to incompressible solution as Mach number approaches zero.
- Convergence holds for well-prepared initial data.
- Provides theoretical validation for the scheme's asymptotic behavior.

## Abstract

We study the incompressible limit of a pressure correction MAC scheme [3] for the unstationary compressible barotropic Navier-Stokes equations. Provided the initial data are well-prepared, the solution of the numerical scheme converges, as the Mach number tends to zero, towards the solution of the classical pressure correction inf-sup stable MAC scheme for the incompressible Navier-Stokes equations.