# Vector penalty-projection method for incompressible fluid flows with open boundary conditions

## Main Article Content

## Abstract

A new family of methods, the so-called vector penalty-projection methods (V PPr;"), were introduced recently by Angot et al. [1, 2] to compute the solution of unsteady incompressible fluid flows and to overcome most of the drawbacks of the usual incremental projection methods. In this work, we deal with the time-dependent incompressible Stokes equations with outflow boundary conditions using the present method. The spatial discretization is based on the finite volume scheme on a MAC staggered grid and the time discretization is based on the backward difference formula of second-order BDF2 (namely also Gear's scheme). We show that the (V PPr;") method provides a second-order convergence for both velocity and pressure in space and time even in the presence of open boundary conditions with small values of the augmentation parameter r; typically 0 · r · 1 and a penalty parameter " small enough; typically " = 10¡10. The resulting constraint on the discrete divergence of velocity is not exactly equal to zero but is satis¯ed approximately as O(" ±t) with a penalty parameter " as small as desired. Finally, the e±ciency and the second-order accuracy of our method are illustrated by several numerical cases.

## Article Details

How to Cite

Angot, P., & Cheaytou, R.
(2015).
Vector penalty-projection method for incompressible fluid flows with open boundary conditions.

*Proceedings Of The Conference Algoritmy,*, 219-229. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/333/239
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