Operator Splitting.

September 16, 2005, 10:35

Hi, I am a student of cfd.

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

Thanks for any help.

September 16, 2005, 15:31

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.

September 17, 2005, 06:12

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.

September 17, 2005, 08:21

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?

September 17, 2005, 10:40

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.

September 17, 2005, 22:10

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.

September 16, 2005, 10:35	Operator Splitting.	#1
Maria. Guest Posts: n/a	Hi, I am a student of cfd. When talking about time discretization schemes, what is meant by operator splitting? Thanks for any help.

September 16, 2005, 15:31	Re: Operator Splitting.	#2
Andrew Hayes Guest Posts: n/a	From what I know, it is splitting the del operator into direction derivative only...ie) if you have (dU/dt)=(-Udel(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.

September 17, 2005, 06:12	Re: Operator Splitting.	#3
muhammad javaid Guest Posts: n/a	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.

September 17, 2005, 08:21	Re: Operator Splitting.	#4
Maria. Guest Posts: n/a	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?

September 17, 2005, 10:40	Re: Operator Splitting.	#5
Runge_Kutta Guest Posts: n/a	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.

September 17, 2005, 22:10	Re: Operator Splitting.	#6
Mani Guest Posts: n/a	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.