2pt0
commented
1 year ago To add a little more context, I am trying to recreate potential flow around a cylinder. The solution should be symmetric about the cylinder.
Here are some image that illustrate what I mean. The only difference between these two simulations is the application of a preconditioner.
With preconditioner (ILU0)
Without preconditioner
The solution without the preconditioner is still not perfect. I'm seeing dissipation likely cause by the grid. Still, the preconditioned solution looks like a viscous flow simulation.
ddemidov
The use of AMG and ILU0 preconditioners is somehow adding dissipation to the solution of the Euler equations discretized with a discontinuous Galerkin (DG) method. This result is particularly interesting because the Euler equations lack a diffusive term.
Solving the Newton system resulting from the DG discretization with and without a preconditioner achieves fundamentally different solutions. Of course, this is to be expected if the system is ill-conditioned. However, the preconditioned solution appears as a viscous flow solution (e.g. formation of a boundary layer, flow separation regions, etc.). When the DG system is solved without preconditioning (i.e. using the Dummy preconditioner), a much more physically consistent solution lacking these viscous effects is achieved.
I recognize the intended effect of preconditioners is to reduce the condition number of the matrix which is directly dependent on the eigenvalues of the matrix. Is there anyway that a preconditioner could act as a "smoother" on the final solution of the system and not just the system itself?
More details: I have ran both GMRES and FGMRES with AMG, ILU0, and Dummy preconditioners. The AMG preconditioners use a V-cycle with smoothed aggregation and SPIA0.