.. _dg-burgers_2D: dg/burgers_2D.py ================ **Description** Burgers equation in 2D solved using discontinous Galerkin method .. math:: \frac{dp}{dt} + div\,f(p) - div(grad\,p) = 0 Based on Kučera, V. (n.d.). Higher order methods for the solution of compressible flows. Charles University. p. 21 eq. (1.39) Usage Examples -------------- Run with simple.py script:: python simple.py examples/dg/burgers_2D.py Results are saved to output/dg/burgers_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:: /../examples/dg/burgers_2D.py