.. _navier_stokes-stabilized_navier_stokes: navier_stokes/stabilized_navier_stokes.py ========================================= **Description** Stabilized Navier-Stokes problem with grad-div, SUPG and PSPG stabilization solved by a custom Oseen solver. The stabilization terms are described in [1]. [1] G. Matthies and G. Lube. On streamline-diffusion methods of inf-sup stable discretisations of the generalised Oseen problem. Number 2007-02 in Preprint Series of Institut fuer Numerische und Angewandte Mathematik, Georg-August-Universitaet Goettingen, 2007. Find :math:\ul{u}, :math:p such that: .. math:: \begin{array}{l} \int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \int_{\Omega} ((\ul{b} \cdot \nabla) \ul{u}) \cdot \ul{v} - \int_{\Omega} p\ \nabla \cdot \ul{v} \\ + \gamma \int_{\Omega} (\nabla\cdot\ul{u}) \cdot (\nabla\cdot\ul{v}) \\ + \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ ((\ul{b} \cdot \nabla) \ul{u})\cdot ((\ul{b} \cdot \nabla) \ul{v}) \\ + \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p\cdot ((\ul{b} \cdot \nabla) \ul{v}) = 0 \;, \quad \forall \ul{v} \;, \end{array} \begin{array}{l} \int_{\Omega} q\ \nabla \cdot \ul{u} \\ + \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ ((\ul{b} \cdot \nabla) \ul{u}) \cdot \nabla q \\ + \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla p \cdot \nabla q = 0 \;, \quad \forall q \;. \end{array} .. image:: /../gallery/images/navier_stokes-stabilized_navier_stokes.png :download:source code  .. literalinclude:: /../examples/navier_stokes/stabilized_navier_stokes.py