.. _diffusion-time_advection_diffusion: diffusion/time_advection_diffusion.py ===================================== **Description** The transient advection-diffusion equation with a given divergence-free advection velocity. Find :math:`u` such that: .. math:: \int_{\Omega} s \pdiff{u}{t} + \int_{\Omega} s \nabla \cdot \left(\ul{v} u \right) + \int_{\Omega} D \nabla s \cdot \nabla u = 0 \;, \quad \forall s \;. View the results using:: python postproc.py square_tri2.*.vtk -b --wireframe .. image:: /../gallery/images/diffusion-time_advection_diffusion.png :download:`source code ` .. literalinclude:: /../examples/diffusion/time_advection_diffusion.py