Making SIMPLE converge faster

Fabio

Hello everybody. I wrote e CFD code for MHD research applications: I look for the equilibrium (i.e. not transient) of a conducting fluid in an externally imposed magnetic field. There is no turbulence (at least not yet), and I am using the SIMPLE algorithm to couple momentum and continuity (an energy equation is also included). I use triangular meshes. My problem comes now: from some numerical experiments I got the feeling that the SIMPLE algorithm have problems to converge on too fine meshes. If I start refining progressively my mesh, I do not say it does not converge at all, but the number of iterations needed seems to increase very much, which I am not happy with if my mesh already have a large number of nodes. I have a couple of questions:

1. Is my feeling correct? Does really the SIMPLE become less efficient on refined meshes? If so, can anybody point me out any literature on the subject?

2. Should the answer to my first question be "YES": how can I circumvent the problem (i.e. accelerating convergence)? At the moment I am choosing relaxation parameters accounting partly accounting for some advices I got in the literature (rel_pressure + rel_momentum not too far from 1), partly for some preliminary tests I made some time ago, but nothing very sistematic. Is it worth to try some more systematic tests? Are there any other techniques on the market? (Once again: is any literature available?)

3. Are there any other algorithm alternative to SIMPLE available? I know this is a silly question: there is plenty of algorithms. However, from the literature I gained the feeling that most of the segregated approaches (SIMPLER, SIMPLEC, PISO) are variations on the same theme, so they should suffer more or less from the same disadvantages. Am I correct? Does it exists anything substantially different (and better)? Where can I look for documentations? And what about coupled approaches (e.g. Newton-Raphson)?

Sorry for a so long set of questions, and thank you in advance. Fabio