Steady state convergence tolerance

[Roland]

Hi,
It is a bit difficult to really understand how all the convergence tolerances interact during the solve only in sentences, Kevin. I saw the ElmerSolverManual's 1.2 part (Handling interactions of multiple physical phenomena) which shows the pseudo-code of the handling of a multiphysics equation systems.
By taking inspiration from this could it be possible to write a kind of extension of such pseudo-code which shows the working of the linear iteration(if iterative solver), then the nonlinear iterations, then the steady_state iterations and at last the time stepping (with the Euler method for instance) for a time-dependant non linear multiphysics equation system. (if I don't mistake the "steady_state" exists both for a non time-dependant and for a time-dependant system)
Say that if we take a non linear time dependant system of 2 equations F1(u1,u2)=0 and F2(u1,u2)=0 (these could be for instance respectively the Heat_transfer equation and the Navier_Stokes equation) , u1 and u2 being the 2 variables, the 2 equations look like something following:
du1/dt+A(u1)*u1=B(u2)
du2/dt+C(u2)*u2=D(u1)
The coupling is done (for instance) by the second members and the non-linearity is given by the 2nd terms of the 1rst members.
After Euler time discretisation (say n+1 is the unknown new time step number and n is the known former time step number) these 2 equations become:
(1-A(u1,n+1))*u1,n+1 = delta_t*B(u2,n) + u1,n
(1-C(u2,n+1))*u2,n+1 = delta_t*D(u2,n) + u2,n
delta_t is the time step (for simplification we can assume that the problem is 1D and that there is only one mesh node)
So could it be possible to write the pseudo-code showing how all the iterations (linear (if iterative solver), nonlinear, steady_state and time stepping) work? (Say that I would do something like that because I don’t yet see the real difference between the non linear treatment of the coupled system and the steady_state.)
Any help would be welcome!
Thanks in advance
Roland

[kevinarden]

Peter is best suited to give a technically explanation but for my limited brain;

strategy 1, which I associate with loose couple
they converge in steps on after another
linear convergence, complete till converged ==> non-linear convergence, complete till converged==> steady state convergence, repeat previous steps till converged


strategy 2, which I associate with more coupling
they converge and go back and forth and converge again before moving on
linear convergence, complete till converged, repeat depending on non-linear ==> non-linear convergence, complete till converged, go back to linear for another check, repeat ==> steady state convergence, repeat previous steps till converged

[Roland]

Hi Kevin,
Thanks again for your valuables efforts!
Yes, what you say with words is exactly what I would translate in pseudo-code!
Do you think that it would possible? Perhaps Peter could also give his opinion.
We keep us informed.
Thanks again!
Roland