@Article{IJNAMB-4-1, author = {T. GORNAK, J.L. GUERMOND, O. ILIEV, AND P.D. MINEV}, title = {A Direction Splitting Approach for Incompressible Brinkman Flow.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2013}, volume = {4}, number = {1}, pages = {1--13}, abstract = {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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/243.html} }