[gigilentini8]

I am bit puzzled by the fact that, for a steady linear differential equation (e.g. advection-diffusion using scalarTransportFoam and steadyState time scheme), OF is not converging in one outer iteration.

I would expect that, in this case, provided that the relative residual in fvSolution is small enough, there would be no need of (pseduo-)time iterations.

am I missing something? what does the steadyState scheme really do?

[hjasak]

steadyState does nothing: it will eliminate the ddt term. However:
- you have possible non-linearity in convection. Use upwind
- you have a deferred correction in diffusion. Make orthogonal mesh

... and it will converge in one call. In fact, it will converge in one preconditioner sweep if you have a trivial 1-D or 2-D mesh.

Hrv

[gigilentini8]

Originally Posted by hjasak

steadyState does nothing: it will eliminate the ddt term. However:
- you have possible non-linearity in convection. Use upwind
- you have a deferred correction in diffusion. Make orthogonal mesh

... and it will converge in one call. In fact, it will converge in one preconditioner sweep if you have a trivial 1-D or 2-D mesh.

Hrv

Thanks Hrvoje,
I actually did not realise I was using a non-orthogonal mesh. However I am still surprised by the relative importance of the "artificial" non-linearities (or deferred corrections in general) introduced. After a time step, the residual was just 1/2 of the original one.

Why simply using linear and uncorrected schemes would not be enough to ensure a simple linear system?

I am asking because I am interested in computing eigenvalues and eigenfunctions and it is of no interest doing that only for orthogonal meshes. I implemented possible workarounds by using the whole OF machinery to solve the system and make use of inverse power iterations to converge to the eigenpair, but it would be nice to directly compute the eigenvalues of a matrix (or generalised eigenvalues more easily)