The Von Neumann stability analysis is used to asses the stability of a transient scheme but cannot be used for a time-independent one. How do I asses the stability and boundedness of a steady state scheme? Particularly, a scheme using the SIMPLE algorithm with the strongly implicit procedure (SIP) for a finite volume method (FVM) with a central differencing scheme (CDS). I don't ask for a full analysis of my particular setup, I'm also happy to do some reading myself but so far I have a hard time finding anything on the stability of an iteration algorithm for steady state systems, let alone anything regarding SIP or CDS for such cases.

Thank you in advance for your answer.

Best regards,

Dimitri