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Convergence results for the vector penalty-projection and two-step artificial compressibility methods

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  • In this paper, we propose and analyze a new artificial compressibility splitting method which is issued from the recent vector penalty-projection method for the numerical solution of unsteady incompressible viscous flows introduced in [1], [2] and [3]. This method may be viewed as an hybrid two-step prediction-correction method combining an artificial compressibility method and an augmented Lagrangian method without inner iteration. The perturbed system can be viewed as a new approximation to the incompressible Navier-Stokes equations. In the main result, we establish the convergence of solutions to the weak solutions of the Navier-Stokes equations when the penalty parameter tends to zero.
    Mathematics Subject Classification: Primary: 35Q30, 76D05, 76N10, 35A35; Secondary: 65M12, 65N12.


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