HDG/DG for time-dependent convection-diffusion equation

Hello,

I had an old NgSolve program solving a nonlinear convection diffusion equation with Robin boundary conditions and wanted to implement it in the newest version. Somehow that does not work ……

I have

→ linear diffusion term - discretised using HDG and treated implicitely in the time-stepping

→ nonlinear convection - discretised with upwind DG and treated explicitely in the time-stepping

→ inflow boundary conditions (“left”) of the form (-\nabla u + u(1-u) e_1) * n = -fin (1-u)

→ outflow boundary conditions (“right”) of the form (-\nabla u + u(1-u) e_1) * n = fout u

→ no flux boundary conditions on “top” and “bottom”

I decided to include the Robin boundary conditions in the system matrix (mass + diffusion + boundary terms), so the inverse should be non-symmetric. The result does not look completely off (some wiggles at the boundary), but I know the stationary profiles, and they do not look at all like what I get.

The minimial example is here:

Pedestrian1.ipynb (4.2 KB)

Thanks a lot!