Workshop on Numerical Methods and Analysis in CFD - Abstract
Kaya, Utku
Pressure-correction methods facilitate approximations of solutions to time-dependent incompressible fluid flows by decoupling the momentum equation from the continuity equation [1]. A common strategy used by several pressure-correction methods is:
(i) compute a (not necessarily divergence-free) predictor velocity field,
(ii) solve a Poisson problem for the pressure,
(iii) project the predictor velocity field onto a divergence-free one.
In cases, where an explicit time-stepping scheme is employed for the momentum equation, the Poisson problem for the pressure remains to be the most expensive step. We here present a domain decomposition method that replaces the pressure Poisson problem from step (ii) with local pressure Poisson problems on non-overlapping subregions [2,3]. No communication between the subregions is needed, thus the method is favorable for parallel computing. We illustrate the effectivity of the method via numerical results.
References:>
[1] J.L. Guermond, P. Minev, J. Shen, An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Engrg. 195:44-47 (2006), 6011--6045.
[2] M. Braack, U. Kaya, Local pressure-correction for the Stokes system. J. Comput. Math. 38:1 (2020), 125--141.
[3] U. Kaya, R. Becker, M. Braack, Local pressure-correction for the Navier-Stokes equations. Internat. J. Numer. Methods Fluids. 93:4 (2021), 1199--1212.