
[Sponsors] 
July 13, 2004, 03:55 
how implicit is implicit?

#1 
Guest
Posts: n/a

Hi, just a general question:
Suppose I have a timedependent 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 predictorcorrector, 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 
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 
Guest
Posts: n/a

How can this 'local mode analysis' be done?


July 13, 2004, 19:15 
Re: how implicit is implicit?

#4 
Guest
Posts: n/a

You can check most numerical analysis text books.
Junseok 

July 14, 2004, 12:18 
Re: how implicit is implicit?

#5 
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 
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 semiimplicit, semiexplicit 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 
Guest
Posts: n/a

Usually we say Crank Nichoson is semiimplicit.


July 16, 2004, 11:10 
Re: how implicit is implicit?

#8 
Guest
Posts: n/a

yeah i think you are right Joe. amol


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Help. implicit discritization  dearboy  Main CFD Forum  0  November 25, 2010 22:46 
Can anyone explain the difference between these implicit concepts?  bearcat  Main CFD Forum  0  February 20, 2010 19:39 
ADI implicit doesn't converge  George Papadakis  Main CFD Forum  2  July 8, 2009 13:27 
implicit vs explicit  pXYZ  Main CFD Forum  2  April 21, 2006 09:48 
UDF : Chemical Reaction in Catalytic Converter  adhimac  FLUENT  1  March 27, 2001 14:04 