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Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
Helsinki University of Technology.
2009 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, no 6, p. 1274-1289Article in journal (Refereed) Published
Abstract [en]

We use low order approximations, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Brinkman's equation of porous media flow, applying an edge stabilization term to avoid locking. In order to handle the limiting case of Darcy flow, when only the velocity component normal to the boundary can be prescribed, we impose the boundary conditions weakly using Nitsche's method [J. Nitsche, Uber ein Variationsprinzip zur Losung von Dirichlet-Problemen bei Verwendung von Teilraumen, die keinen Randbedingungen unterworfen sind, Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 36 (1971) 9-15]. We show that this leads to a stable method for all choices of material parameters. Finally we present some numerical examples verifying the theoretical predictions and showing the effect of the weak imposition of boundary conditions. 

Place, publisher, year, edition, pages
2009. Vol. 59, no 6, p. 1274-1289
Keywords [en]
Brinkman model, Stokes-Darcy model, Stabilized methods, Finite element, Interior penalty method, Nitsche's method
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hj:diva-15821DOI: 10.1016/j.apnum.2008.07.003ISI: 000265335900009OAI: oai:DiVA.org:hj-15821DiVA, id: diva2:440333
Available from: 2011-09-12 Created: 2011-08-16 Last updated: 2017-12-08Bibliographically approved

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Hansbo, Peter

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