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

Finite Volume Method

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

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   April 9, 2016, 15:18
Default Finite Volume Method
  #1
Member
 
Join Date: Apr 2016
Posts: 30
Rep Power: 10
shanvach is on a distinguished road
Hi,
Could someone help with a little problem that i have regarding how FVM is applied in CFD.

After discretization,we assume a general function that can be first order upwind,second order upwind etc.How to decide which kind of function to take?

And also what are the effects of larger cell size in FVM?
shanvach is offline   Reply With Quote

Old   April 10, 2016, 09:43
Default
  #2
Senior Member
 
Michael Prinkey
Join Date: Mar 2009
Location: Pittsburgh PA
Posts: 363
Rep Power: 25
mprinkey will become famous soon enough
First order upwind assumes that the solution is piecewise constant over the cells...the value at the each face is the same as value at the centroid. Second order upwind assumes a linear expansion with the centroid value being the cell-averaged value and the linear terms as the gradient of the function dotted with the vector connecting the cell centroid to the test location:

phi(x) = phi_c + grad(phi) . (x - x_c)

Formal order of accuracy is important, but really, the use of higher order schemes, especially for advection/convection terms is governed by artificial diffusion. First-order upwind schemes are very diffusive, so you lose details very quickly in practical simulations.

Errors scale in FVM as they do in finite difference, finite element, or even plain-old Talyor series expansions. Errors increase as you make FV larger. The rate of increase is governed by the order of the method. First-order schemes scale error linearly. Second-order sceheme scale error quadratically, etc.
mprinkey is offline   Reply With Quote

Old   April 11, 2016, 05:41
Default
  #3
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,887
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by shanvach View Post
Hi,
Could someone help with a little problem that i have regarding how FVM is applied in CFD.

After discretization,we assume a general function that can be first order upwind,second order upwind etc.How to decide which kind of function to take?

And also what are the effects of larger cell size in FVM?

The FV is based on the integral form of the equation. The function you are referring is the numerical flux function. Upwind (first, second or higher) flux has intrinsically numerical viscosity (mprinkey already wrote) while central flux discretizations have not. What you use depends on the flow case and formulation. DNS/LES use discretization without numerical viscosity conversely RANS use also upwind.
FMDenaro is offline   Reply With Quote

Old   April 11, 2016, 05:48
Default upwind scheme for Euler equation
  #4
Member
 
sajad
Join Date: Apr 2014
Location: Iran
Posts: 46
Rep Power: 12
sajad6 is on a distinguished road
Does upwind scheme cause problem for Euler equation?
sajad6 is offline   Reply With Quote

Old   April 11, 2016, 05:54
Default
  #5
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,887
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by sajad6 View Post
Does upwind scheme cause problem for Euler equation?

For Euler equations the upwind discretization is used, often for the characteristic-based variables. You can find details in the book of Leveque
FMDenaro is offline   Reply With Quote

Old   May 21, 2016, 03:28
Default
  #6
Member
 
LUQILIN
Join Date: May 2016
Location: Harbin, China
Posts: 35
Rep Power: 10
LUQILIN is on a distinguished road
Quote:
Originally Posted by shanvach View Post
Hi,
Could someone help with a little problem that i have regarding how FVM is applied in CFD.

After discretization,we assume a general function that can be first order upwind,second order upwind etc.How to decide which kind of function to take?

And also what are the effects of larger cell size in FVM?
1. It depends what problem you are dealing with. Generally 1st order scheme is too dissipate. But you should try it first to totally understand its meaning. Just use the center value of element then you can get a 2nd order scheme. Do a accuracy test after you finish your code and make sure 2nd order is achieved.
What you say about upwind is the way to compute flux at cell interface when discrete convention terms.

2. You can test the effects of cell size yourself. But if time integration is an explicit scheme, the cell size is not independent, i.e., associated with time steps. Check CFL number and ensure that your scheme is stable.
LUQILIN is offline   Reply With Quote

Reply

Tags
discretization, function, fvm, node, size

Thread Tools Search this Thread
Search this Thread:

Advanced Search
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 Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
[blockMesh] error message with modeling a cube with a hold at the center hsingtzu OpenFOAM Meshing & Mesh Conversion 2 March 14, 2012 10:56
On the damBreak4phaseFine cases paean OpenFOAM Running, Solving & CFD 0 November 14, 2008 22:14
[blockMesh] Axisymmetrical mesh Rasmus Gjesing (Gjesing) OpenFOAM Meshing & Mesh Conversion 10 April 2, 2007 15:00
ALE in finite volume method littlelz Main CFD Forum 5 June 21, 2003 13:50
finite volume method for CFD analysis of 2D blunt body Aditya Vaze Main CFD Forum 1 January 19, 2000 14:55


All times are GMT -4. The time now is 04:10.