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 Maria. September 16, 2005 10:35

Operator Splitting.

Hi, I am a student of cfd.

When talking about time discretization schemes, what is meant by operator splitting?

Thanks for any help.

 Andrew Hayes September 16, 2005 15:31

Re: Operator Splitting.

From what I know, it is splitting the del operator into direction derivative only...ie) if you have (dU/dt)=(-U*del(U)) and you wanted to split for 2-D you would end up with

1) dUx/dt=-Ux*(dU/dx)

and

2) Duy/dt=-Uy*(dU/dx)

it saves on computational time. Then again, with some of the modern stout computers it might not really matter.

 muhammad javaid September 17, 2005 06:12

Re: Operator Splitting.

Fractional Operator technique (also known as Splitting Algorithm) is very useful and commonly used technique in CFD and Air pollution modeling. It is economical in solving convection dominated flow equations. Read PDEs chapter of NUMERICAL RECEIPES by Press for a short introduction. Also download PDF 'collis-cfm-sand'which is SANDIA REPORT SAND2005-XXXX April 26, 2005.

 Maria. September 17, 2005 08:21

Re: Operator Splitting.

Hi,

Thank you. If I am solving in 2D, are you saying that I will solve equation 1 first and then equation 2? What is special about this?

 Runge_Kutta September 17, 2005 10:40

Re: Operator Splitting.

Maria,

This maybe too much but try looking at this article and anyone who references it:

http://www.sciencedirect.com/science...6c6e5996361d12 Vol. 111, No. 1-2 (1999) 201-216.

In contrast to a decoupled intergration approach, also consider a coupled approach via something like:

http://www.sciencedirect.com/science...3bd4e2b895b496 vol. 37, No. 4 (2001) 535-549.

or

http://portal.acm.org/citation.cfm?i...TOKEN=58991849

Coupled approaches should always be preferred if all other things are equal.

 Mani September 17, 2005 22:10

Re: Operator Splitting.

The "special" thing about it is the treatment of both parts independently (although they implicitly depend on each other).

In the general sense, operator splitting is to take a multi-dimensional operator and describe it as a sequence of one-dimensional operators. You can then iteratively solve your equations by considering each dimension (each operator) in sequence, while freezing all other operations. "Dimension" could mean spatial or temporal dimension or could also stand for various phenomena like advection, diffusion, chemical reaction, and so on...

This practice greatly simplifies the numerical algorithm and increases efficiency at the expense of inter-dimensional coupling (which may lower the accuracy). You should probably look at an example to understand that.

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