I am working on implicit schemes for Euler equations. Implicit methods allow one to use large CFL values, but is there some way to evolve CFL number from a much smaller value than desired value to avoid errors in initial iterations. There are some strategies available in literature, such as exponential increment.

CFL evolution strategy directly affects time for computation, and I want to minimize the time consumption. Is there any standard way to evolve CFL number? Or is it done by trial and error?

  • $\begingroup$ Welcome to SciComp! This question isn't terribly clear, and it seems broad. Could you please clarify what you mean and narrow the scope of your question? (You should be able to edit your question while it is closed; I'll reopen the question once it is rewritten for clarity and scope.) $\endgroup$ Apr 26, 2013 at 6:07
  • $\begingroup$ Sir, I have tried to make it clear now. Thanks for suggestion. $\endgroup$
    – Shainath
    Apr 26, 2013 at 6:35
  • $\begingroup$ It's hard to answer this question without knowing what kind of constraints with regard to, e.g. accuracy, you're working with. Implicit schemes for the Euler equations are going to introduce a significant amount of artificial dissipation, and they aren't going to net a greatly improved CFL as you already have $dx = \mathcal O(dt)$ for explicit schemes. $\endgroup$
    – Ben
    Apr 26, 2013 at 15:22
  • $\begingroup$ @JohnDelong I don't want to discuss about effects of large CFL values on solution. Here question is what strategy one should use to evolve CFL in case of implicit schemes. As you mentioned there are some drawbacks of very high CFL values, but first I should get answer to investigate it. $\endgroup$
    – Shainath
    Apr 28, 2013 at 6:52

1 Answer 1


Your question is correct, but this is still an open problem (see paper here). There are many methods to evolve CFL value in case of implicit methods. Every method has its own advantages and disadvantages. Choose the strategy which satisfies your needs or otherwise you can introduce efficient new strategy and publish it. All the best.

  • $\begingroup$ Thanks for your answer. Just one day ago I came across this paper. Thanks for your suggestions. $\endgroup$
    – Shainath
    Apr 29, 2013 at 6:25

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