.. _dg-advection_diffusion_2D: dg/advection_diffusion_2D.py ============================ **Description** Static advection-diffusion equation in 2D solved by discontinous Galerkin method. .. math:: a \cdot grad\, p - div(grad\,p) = 0 Based on Antonietti, P., & Quarteroni, A. (2013). Numerical performance of discontinuous and stabilized continuous Galerkin methods for convection-diffusion problems. Usage Examples -------------- Run:: sfepy-run sfepy/examples/dg/advection_diffusion_2D.py Results are saved to output/dg/advection_diffusion_2D folder by default as ` `.msh`` files, the best way to view them is through GMSH (http://gmsh.info/) version 4.6 or newer. Start GMSH and use ``File | Open`` menu or Crtl + O shortcut, navigate to the output folder, select all ``.msh`` files and hit Open, all files should load as one item in Post-processing named p_cell_nodes. GMSH is capable of rendering high order approximations in individual elements, to modify fidelity of rendering, double click the displayed mesh, quick options menu should pop up, click on ``All view options...``. This brings up the Options window with ``View [0]`` selected in left column. Under the tab ``General`` ensure that ``Adapt visualization grid`` is ticked, then you can adjust ``Maximum recursion depth`` and ```Target visualization error`` to tune the visualization. To see visualization elements (as opposed to mesh elements) go to ``Visibility`` tab and tick ``Draw element outlines``, this option is also available from quick options menu as ``View element outlines`` or under shortcut ``Alt+E``. In the quick options menu, you can also modify normal raise by clicking ``View Normal Raise`` to see solution rendered as surface above the mesh. Note that for triangular meshes normal raise -1 produces expected raise above the mesh. This is due to the opposite orientation of the reference elements in GMSH and Sfepy and might get patched in the future. :download:`source code ` .. literalinclude:: /../sfepy/examples/dg/advection_diffusion_2D.py