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Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow

Peter Hansbo (Institutionen för matematiska vetenskaper, matematik) ; M. Juntunen
Applied Numerical Mathematics (0168-9274). Vol. 59 (2009), 6, p. 1274-1289.
[Artikel, refereegranskad vetenskaplig]

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, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abhandlungen aus dem Mathematischen Seminar der Universität 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.

Nyckelord: Brinkman model, Stokes–Darcy model, Stabilized methods, Finite element, Interior penalty method, Nitsche's method



Denna post skapades 2009-03-31. Senast ändrad 2016-08-15.
CPL Pubid: 92030

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys
Strömningsmekanik

Chalmers infrastruktur