Mathematical derivation of SIMPLE etc.
 

Hi,

are the any mathematical derivations/proofs which show that the algorithms like SIMPLE/SIMPLER/PISO are working? I can only find the original papers but I don't like to buy them till I know that this mathematical stuff is included.

Best Regards,

Za-ck

I don't think there are any proofs. Like all other non-linear solvers (at least that I know) I think you can not show that they converge for every case. As far as I know, this (showing convergence) only works with really simple cases, such as linear problems.

I don't know about the specific algorithms above, but YOU CAN show stability and convergence for nonlinear solvers.
In fact I'm pretty sure you must show stability and convergence of any new solver.
CFX for example is unconditionally stable///

This statement does not make any sense. CFX is a software tool with tons of different numerical methods.
Please go to CFX and set under relaxation factor for pressure to 100 in SIMPLE. See what happens.

Could you better formulate your question? what do you mean with "are working"? Discrete formulations that are consistent and stable must always work ...