How to choose the CFL number with implicit scheme?
 

We know the CFL numerber must be less 1 when solve the Euler or NS equations with explicit scheme. Although the imiplicit scheme is unconditional stable, the the CFL can not allow infinite in computation.So when we solve thesse eqations with imiplicit scheme, How much CFL numerber is fit for problem?

Re: How to choose the CFL number with implicit sch
 

"Although the imiplicit scheme is unconditional stable" - instability may also arise from boundary conditions.

Re: How to choose the CFL number with implicit sch
 

You are right, the scheme is unconditionally stable. But this does not mean that it is unconditionally accurate! Just like you need a fine grid to resolve your length scales in certain areas of the domain, you need also a fine time step to resolve your physical processes in time in relevant areas. In many cases, the accuracy will not be much affected by taking a larger time step, but in some cases, it may make a large difference.

So I would say there is no general answer apart from: stick to a CFL number close to unity, and your chances look fair. In many cases, typically 5 would also be OK. But of course, the information in the info-file is not alone enough to judge this (max CFL and average CFL). You may well allow a CFL number of, say, 20 in some areas of your domain, if they are away (and downstream?) from your main interest area. You need to know your local CFL numbers, which can be extracted from an analyses by the .err file.