CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Implicit vs Explicit method

Register Blogs Community New Posts Updated Threads Search

Like Tree52Likes
  • 35 Post By Tom
  • 2 Post By Jim Park
  • 10 Post By dimitri
  • 4 Post By Ford Prefect
  • 1 Post By bouloumag

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   April 11, 2003, 02:17
Default Implicit vs Explicit method
  #1
Donna
Guest
 
Posts: n/a
Dear all,

I'm a university student who just jump into the field of CFD. Would you please tell me the definitions of implicit method and explicit method? And what are the differences for their usage? Last question is that what is the important factor for my decision of using either one? Thank you for your help!

Donna
  Reply With Quote

Old   April 11, 2003, 05:41
Default Re: Implicit vs Explicit method
  #2
Tom
Guest
 
Posts: n/a
Basically an explicit scheme is one where there is a simple updating procedure that does not depend upon other values at the current level while an implicit one contains information at the current level which requires the solving of simultaneous equations.

For example consider the the system of odes

du/dt = f(u)

where u is a vector and f is a known function. Then we may approximate the time derivative over a time step h as

(explicit) u(n+1) = u(n) + h.f(u(n))

(implicit) u(n+1) = u(n) + h.f(u(n+1))

where u(n) is the value of u at t=nh. In the explicit formula the right-hand-side is known and so u(n+1) is easily calculated while in the implicit case the RHS depends upon the quantity you are trying to calculate. If f(u) = Au where A is a matrix independent of u then the implicit scheme requires solving the system of equations

(I-hA).u(n+1) = u(n)

and so a matrix inversion needs to be performed.

The main pros and cons of these two methods are that explicit schemes are easy to program with only simple calculations performed at each timestep while implicit schemes are more difficult and can involve many iterations per timestep. Explicit schemes however have a tendancy to be unstable and require very small timesteps while implicit schemes are very stable and can have much larger timesteps.

The book

Numerical solution of partial differential equations by G.D. Smith (1979). Oxford University Press

is worth looking at (if it's still in print) for a basic introduction to numerical analysis.
Far, vishnujbr, DungPham and 32 others like this.
  Reply With Quote

Old   April 11, 2003, 11:46
Default Re: Implicit vs Explicit method
  #3
Jim Park
Guest
 
Posts: n/a
"and so a matrix inversion needs to be performed."

To nitpick a little, the matrix doesn't need to be inverted to solve the system for u(n+1); what is needed is to solve the system of simultaneous equations.

This can still be a daunting task, but generally quite a bit less computational work than taking the inverse.

Otherwise, I think Tom's response, and advise, is dead on. Good luck with your problem.

aerosayan and fan01 like this.
  Reply With Quote

Old   April 11, 2003, 19:32
Default Re: Implicit vs Explicit method
  #4
dimitri
Guest
 
Posts: n/a
Tom's explanation is very good!

Now what does it mean for you? If you try to solve low frequencies problems (the lowest being steady state) go for implicit because you only need a few long time steps. If you try to solve medium high frequencies problems go for explicit because a small time step is required anyway and the cost of each time step is way lower with explicit.

Exemples of typical applications: CFD steady state = implicit Aero-Acoustics and highly transient flows = explicit

Structural static analysis = implicit Structural crash analysis = explicit

I would dare say that: f >100Hz -> go explicit f between 100 and 2 Hz grey zone (explicit and implicit can compete) f < 2Hz -> go implicit

Notable exception: weather forecast which is performed with explicit schemes but such big elements size that the time step is OK.

Dimitri
  Reply With Quote

Old   April 13, 2003, 04:46
Default Re: Implicit vs Explicit method
  #5
Donna
Guest
 
Posts: n/a
Dear Tom, Jim Park & dimitri,

Thank you for your responses and explanations. All those are beneficial to me. Thanks a lot! =)

Donna
  Reply With Quote

Old   September 13, 2019, 14:33
Default
  #6
New Member
 
Mathhew B
Join Date: Sep 2019
Posts: 1
Rep Power: 0
MachCone is on a distinguished road
Quote:
Originally Posted by dimitri
;24103
Tom's explanation is very good!

Now what does it mean for you? If you try to solve low frequencies problems (the lowest being steady state) go for implicit because you only need a few long time steps. If you try to solve medium high frequencies problems go for explicit because a small time step is required anyway and the cost of each time step is way lower with explicit.

Exemples of typical applications: CFD steady state = implicit Aero-Acoustics and highly transient flows = explicit

Structural static analysis = implicit Structural crash analysis = explicit

I would dare say that: f >100Hz -> go explicit f between 100 and 2 Hz grey zone (explicit and implicit can compete) f < 2Hz -> go implicit

Notable exception: weather forecast which is performed with explicit schemes but such big elements size that the time step is OK.

Dimitri
Hey Dimitri,

In weather forecast, don't we use a large time step(like 12h for example). So going by the rule, shouldn't we use Implicit method?
MachCone is offline   Reply With Quote

Old   September 13, 2019, 18:30
Default
  #7
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,849
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by MachCone View Post
Hey Dimitri,

In weather forecast, don't we use a large time step(like 12h for example). So going by the rule, shouldn't we use Implicit method?



Who told you that in weather forecast a 12h time step is used??
FMDenaro is online now   Reply With Quote

Old   September 16, 2019, 16:28
Default
  #8
Senior Member
 
Ford Prefect's Avatar
 
Join Date: Mar 2009
Posts: 157
Rep Power: 17
Ford Prefect is on a distinguished road
The more interesting question here is if Dimitri will answer this question 16 years later
__________________
"Trying is the first step to failure." - Homer Simpson
Ford Prefect is offline   Reply With Quote

Old   October 19, 2019, 00:33
Default exponential integrators
  #9
New Member
 
Christine Darcoux
Join Date: Jul 2011
Posts: 15
Rep Power: 15
bouloumag is on a distinguished road
Exponential integrators are a very interesting class of EXPLICIT schemes allowing very large time step size (much larger than the cfl condition).

Christine
arjun likes this.
bouloumag is offline   Reply With Quote

Reply


Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Implicit iterative Gauss-Seidel method dearboy Main CFD Forum 5 November 29, 2010 10:18
Explicit vs Implicit method in free surface flow Farhad Main CFD Forum 4 November 16, 2006 11:42
Euler (explicit or implicit) anybody Main CFD Forum 2 May 8, 2006 03:12
implicit vs explicit pXYZ Main CFD Forum 2 April 21, 2006 10:48
Implicit method of FSI cjtune Siemens 0 March 12, 2003 13:07


All times are GMT -4. The time now is 14:27.