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how implicit is implicit?

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Old   July 13, 2004, 03:55
Default how implicit is implicit?
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Joe cool
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Hi, just a general question:

Suppose I have a time-dependent partial differential equation and would like to discretise (temporally) it into an implicit form. Does that mean that the time step size that I choose will not affected by the grid size that I choose to discretise my spatial derivatives?

Or will I also have to consider the method that I choose to solve my implicit form? Suppose, instead of solving simultaneously all the unknowns under one large matrix, I choose an iterative method, like a multiple predictor-corrector, will my time step size be more restricted then(as like in an explicit form of temporal discretisation)?
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Old   July 13, 2004, 04:03
Default Re: how implicit is implicit?
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Junseok Kim
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Even if your disretization is implicit, if the solver is iterative, then you have time step size restriction. You can estimate that with local mode analysis.

Junseok
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Old   July 13, 2004, 19:05
Default Re: how implicit is implicit?
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Cool Joe.
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How can this 'local mode analysis' be done?
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Old   July 13, 2004, 19:15
Default Re: how implicit is implicit?
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Junseok Kim
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You can check most numerical analysis text books.

Junseok
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Old   July 14, 2004, 12:18
Default Re: how implicit is implicit?
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amol palekar
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Hi, I guess the highest speed of local disturbance is critical. I think the delta_x/delta_t of the computational domain must be smaller than the physical speed of disturbances. So for the same grid size, time step has to be smaller for a shock wave of say Mach 3 then the Mach 1.5 wave. You can verify this with any one dimensional moving shock problem. -amol
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Old   July 15, 2004, 20:54
Default Re: how implicit is implicit?
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Joe cool
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Ok, great, thanks all!

I'm trying to sort this out.. so I should say that even though the scheme is implicit, it really has to depend on how the scheme is solved. But I suppose the time size restriction has to be looser than that of an explicit scheme, right?

Can anyone verify with me if a Crank Nicolson 2nd order time discretization is a semi-implicit, semi-explicit scheme?

And, amol, I'm doing an incompressible flow of low to medium Re. So for this local speed, I should be using the maximum |(U,V)| within the domain, right? I suppose this is basically the CFL criterion.
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Old   July 16, 2004, 01:02
Default Re: how implicit is implicit?
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Junseok Kim
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Usually we say Crank Nichoson is semi-implicit.

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Old   July 16, 2004, 11:10
Default Re: how implicit is implicit?
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amol
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yeah i think you are right Joe. -amol
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