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stability/boundedness of CDS in st.st. FVM

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Old   June 19, 2020, 17:48
Default stability/boundedness of CDS in st.st. FVM
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dimitri koletsos
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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
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Old   June 19, 2020, 18:16
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Filippo Maria Denaro
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Quote:
Originally Posted by dkoletsos View Post
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.
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Old   June 19, 2020, 19:56
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Originally Posted by FMDenaro View Post
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.

Last edited by dkoletsos; June 20, 2020 at 17:28.
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