[dkoletsos]

Hi all,
From what I understand the Von Neumann stability analysis is used to assess the stability of finite difference schemes and the condition for conditionally stable schemes like the central differencing scheme (CDS) involves a critical timestep. I have two questions:
1. Can the Von Neumann analysis be used for finite volume analysis FVM and if so, would the analysis for CDS in FVM be identical to that of the finite difference method FDM?
2. How does a steady state simulation affect the condition regarding the timestep? Will a conditionally stable scheme be stable or unstable?

Thank you in advance for your answer.

Best regards,
Dimitri

[FMDenaro]

Originally Posted by dkoletsos

Hi all,
From what I understand the Von Neumann stability analysis is used to assess the stability of finite difference schemes and the condition for conditionally stable schemes like the central differencing scheme (CDS) involves a critical timestep. I have two questions:
1. Can the Von Neumann analysis be used for finite volume analysis FVM and if so, would the analysis for CDS in FVM be identical to that of the finite difference method FDM?
2. How does a steady state simulation affect the condition regarding the timestep? Will a conditionally stable scheme be stable or unstable?

Thank you in advance for your answer.

Best regards,
Dimitri

1) Yes, it applies to the resulting algebric system both for FD and FV methods. The results of the stability constraint depends on the resulting algebric system, that is not an issue of FV or FD scheme.
2) without time step (steady formulation) there is not stability analysis in the von Neumann sense. You have to see the constraint for the convergence of the iterative method.

[dkoletsos]

Originally Posted by FMDenaro

1)You have to see the constraint for the convergence of the iterative method.

Thank you for your answer.

I'm using the SIMPLE algorithm with the strongly implicit procedure (SIP) for the decomposition. I can only find that this method converges quickly, but not on how the central differencing might affect its stability.