Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows
Provides theoretical justification for using a compressible scheme in nearly incompressible regimes, relevant for numerical analysts working on fluid dynamics.
The paper proves that a pressure correction MAC scheme for compressible barotropic flows converges to the incompressible Navier-Stokes solution in the low Mach number limit, given well-prepared initial data.
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.