About the difference between ac-navier-stokes and navier-stokes

Dear all,

Thank your always supports.
I would like to know the difference between ac-navier-stokes and navier-stokes in detail.
Could you please let me know ? If there are available journal papers, could you attach papres in Paper - Google Drive or give me URL?

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navier-stokes solves the full compressible Navier–Stokes equations. See section 4 of this paper for an example: https://doi.org/10.1016/j.compfluid.2021.104922

ac-navier-stokes solves a formulation of Navier–Stokes called the artifical compressibility Navier–Stokes. This system approximates solutions to the incompressible Navier–Stokes equations. See this paper for more details: https://doi.org/10.1016/j.compfluid.2022.105634

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