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Home Forums CFD foundation course: Forum Courant Number

  • Posted by DEEPANKER CHAUDHARY on March 13, 2024 at 5:44 pm

    It is mentioned in the lecture that the Courant number should be less than 1 for convection-diffusion problems. I have some questions regarding this statement. Does this number have any meaning in steady-state problems? And does the critical value of 1 depend on whether an explicit or implicit scheme is used?

    Sujith FTL replied 2 months, 4 weeks ago 2 Members · 1 Reply
  • 1 Reply
  • Sujith FTL

    Member
    March 18, 2024 at 8:29 am

    Hello,

    In steady-state problems, the Courant number may not have a direct interpretation in terms of time evolution since the system is not changing with time. However, the Courant number can still have relevance, especially if the steady-state solution is obtained through a time-stepping numerical method. In such cases, the Courant number may affect the stability and accuracy of the numerical solution, even though the system itself is not evolving in time.

    The critical value of the Courant number being less than 1 is a general guideline for stability in explicit time-stepping schemes, especially in problems involving convection-diffusion equations. However, for implicit schemes, the stability criterion is typically more relaxed, and the critical value of the Courant number may not be as stringent. Implicit schemes often allow larger time steps since they inherently account for future behavior, making them more stable for a wider range of Courant numbers.

    Regards,

    Sujith

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