On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes
Mathematics of Computation
A finite element penalty-projection method for incompressible flows
Journal of Computational Physics
On the penalty-projection method for the Navier-Stokes equations with the MAC mesh
Journal of Computational and Applied Mathematics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
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In a previous work (Angot et al. in J. Comput. Appl. Math. 226:228---245, 2009), some penalty---projection methods have been tested for the numerical analysis of the Navier-Stokes equations. The purpose of this study is to introduce a variant of the penalty---projection method which allows us to compute the solutions faster than by using the previous solver. This new variant combines dynamically and alternatively a penalty procedure and a projection procedure according to the size of the divergence of the velocity. In other words, this study aims to prove that it is possible to project the intermediate velocity, computed by the first step of the penalty---projection method, only if its divergence is larger than a specified threshold. Theoretical estimates for the new method are given, which are in accordance with the numerical results provided.