Strategies (solver, etc) for advection-diffusion equation

Question

Dear All,

I have been trying to solve a steady state advection diffusion equation over the last weeks and have reached ok but not good enough results.

One problem I have is that the fenics solver does not converge from one point onwards when I increase(!) the mesh resolution.

I would be grateful if somebody had some general advice, for example, which solvers with which preconditioners may work best for this type of problem etc.

Thank you and best wishes,
Merlin :)

Comments

Hello,

Just something you mihgt want to think about... increasing the mesh resolution directly implies that you need to decrease your time step for each iteration..

Here you find a fully function working example provided...

Regards,
Leonardo

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Hey Leonardo,

Thank you for your feedback. I actually try to solve a steady state ADE, thus, there is no issue with the time steps. Indeed, my solutions actually agree quite well with some analytical solutions for my particular problem - nevertheless, further increases in resolution leads to convergence issues.

The other problem I have is that when I increase the Peclet number the results become worse and worse. From what I understand a Petrov Galerkin formulation should help there... however, my question was aiming on getting maybe a fenics example for that...

Thank you for the link to the example, though.
Best wishes,
Merlin :)