TY - JOUR
T1 - A Direction Splitting Approach for Incompressible Brinkman Flow.
AU - T. GORNAK, J.L. GUERMOND, O. ILIEV, AND P.D. MINEV
JO - International Journal of Numerical Analysis Modeling Series B
VL - 1
SP - 1
EP - 13
PY - 2013
DA - 2013/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/243.html
KW - Direction splitting
KW - Navier-Stokes-Brinkman equations
AB - The direction splitting approach proposed earlier in [7], aiming at the efficient solution of Navier-Stokes equations, is extended and adopted here to solve the Navier-Stokes-Brinkman
equations describing incompressible flows in pure fluid and in porous media. The resulting pressure 
equation is a perturbation of the incompressibility constraint using a direction-wise factorized
operator as proposed in [7]. We prove that this approach is unconditionally stable for the unsteady 
Navier-Stokes-Brinkman problem. We also provide numerical illustrations of the method's
accuracy and effciency.