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

Computational complexity of Navier Stokes equations

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   May 3, 1999, 11:41
Default Computational complexity of Navier Stokes equations
  #1
Marco Ellero
Guest
 
Posts: n/a
Usually , in a simulation of an uncompressible fluid, it used a CFD technique (finite differences, volume,etc..), anyway the physical domain of the fluid is divided in cells. It is also necessary to solve the Poisson equation for the pressure, wich rapresent the most slow calcuus process. I wish to know wich is the dependence of the computational complexity from the number of cells in the domain (N^2,NlogN?) Thanks
  Reply With Quote

Old   May 3, 1999, 12:36
Default Re: Computational complexity of Navier Stokes equations
  #2
John C. Chien
Guest
 
Posts: n/a
(1). How do you define the computational complexity? (2). Since it is necessary to study the mesh-independence issue of the solution, the number of cells must be increased in the study. With more cells to solve, it will take longer to compute the flow field. (3). The convergence of the solution depends on the methods used, such as the point-iterative method, the line-iterative method or the direct solution method. It probably depends on the problem itself, I think.
  Reply With Quote

Old   May 3, 1999, 13:33
Default Re: Computational complexity of Navier Stokes equations
  #3
Marco Ellero
Guest
 
Posts: n/a
1) I define it so: the number of step wich the machine need to do ( after one time step ) to calculate the pressure in all domain (for every cell). If we want to calculate the pressure in one cell , in a Poisson equation, we need to know the values of pressure on all boundary, yes? For example in a box , I think in the worst case, if we divide the domain in N cells , we shoul need N^2 step for every time step. Maybe this is improved by use of particular techniques. Anyway, isn't there an inferior limit ? I know it depends on the problem, but in a general case of a box where I solve a Poisson equation?
  Reply With Quote

Old   May 3, 1999, 13:58
Default Re: Computational complexity of Navier Stokes equations
  #4
John C. Chien
Guest
 
Posts: n/a
(1)For every time step, you have to update the pressure at every cell. Since you have divided the domain into N cells, you have to update the pressure at N cells, right? Why N^2 steps?
  Reply With Quote

Old   May 4, 1999, 00:23
Default Re: Computational complexity of Navier Stokes equations
  #5
Tareq Al-shaalan
Guest
 
Posts: n/a
You do not need the pressure on the boundary, if you know teh velocities. it depends on the the method you are using, mostly you could use dp/dn = 0, when teh velocities are known.
  Reply With Quote

Old   May 5, 1999, 21:07
Default Re: Computational complexity of Navier Stokes equations
  #6
Rashid Faizullin
Guest
 
Posts: n/a
If you'll solve your problem in (u,v,w,p) then you should solve Neimann problem for Poissonn equation on every time step i. But if you'll solve in stream functions and etc lang then you should solve Neimann plus Poisonn only one. Of course boundary conditions will be more comlex.

Also you can solve Neimann problem with correction on every time step i: $P^i- \int_{Omega} P^i$ then you will have only CNlogN operations.
  Reply With Quote

Reply

Thread Tools
Display Modes

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 On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
4th order Runge-Kutte & uncoupled method Navier Stokes equations misabel Main CFD Forum 0 February 10, 2010 07:06
Navier Stokes equations in rotation frame..? vinayender Main CFD Forum 2 December 1, 2009 01:12
LBM Vs navier stokes equations in turbulent fluid flow modeling. sharad_shevate Main CFD Forum 0 August 3, 2009 01:25
Presure range of the Navier Stokes Equations Dr. Tsimento Main CFD Forum 7 May 23, 2001 10:12
Navier Stokes Equations J.J. Main CFD Forum 2 June 29, 2000 09:31


All times are GMT -4. The time now is 11:08.