On a new pseudocompressibility method for the incompressible Navier-Stokes equations Original Research Article

We propose and analyze a new pseudocompressibility method which is obtained by introducing a pressure stabilizing/regularizing term in the equation of mass conservation. The perturbed system can be viewed as an approximation to the incompressible Navier-Stokes equations, and its discretization can lead to efficient and accurate numerical schemes for the Navier-Stokes equations. An error analysis for a related artificial compressibility method for the Navier-Stokes equations is also carried out.