## A direction splitting approach for incompressible Brinkmann flow

• The direction splitting approach proposed earlier in [6], 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 plain and in porous media. The resulting pressure equation is a perturbation of the incompressibility constrained using a direction-wise factorized operator as proposed in [6]. 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 efficiency.

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Author: T. Gornak, J. L. Guermond, O. Iliev, P. D. Minev urn:nbn:de:hbz:386-kluedo-33182 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (216) Report English 2012/10/11 2012 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2012/10/11 16 Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vom 10.09.2012

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