# how implicit is implicit?

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 July 13, 2004, 03:55 how implicit is implicit? #1 Joe cool Guest   Posts: n/a 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)?

 July 13, 2004, 04:03 Re: how implicit is implicit? #2 Junseok Kim Guest   Posts: n/a 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

 July 13, 2004, 19:05 Re: how implicit is implicit? #3 Cool Joe. Guest   Posts: n/a How can this 'local mode analysis' be done?

 July 13, 2004, 19:15 Re: how implicit is implicit? #4 Junseok Kim Guest   Posts: n/a You can check most numerical analysis text books. Junseok

 July 14, 2004, 12:18 Re: how implicit is implicit? #5 amol palekar Guest   Posts: n/a 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

 July 15, 2004, 20:54 Re: how implicit is implicit? #6 Joe cool Guest   Posts: n/a 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.

 July 16, 2004, 01:02 Re: how implicit is implicit? #7 Junseok Kim Guest   Posts: n/a Usually we say Crank Nichoson is semi-implicit.

 July 16, 2004, 11:10 Re: how implicit is implicit? #8 amol Guest   Posts: n/a yeah i think you are right Joe. -amol

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