CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

Implicit boundary conditions

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

Like Tree1Likes
  • 1 Post By kalyan

LinkBack Thread Tools Display Modes
Old   February 23, 2001, 15:05
Default Implicit boundary conditions
Atit Koonsrisuk
Posts: n/a
Dear sir, I have read from one paper refer about implicit boundary conditions. What does it mean? Is there the explicit boundary conditions? How can we apply it to our code? Thank you very much sir.

Atit Koonsrisuk.
  Reply With Quote

Old   February 23, 2001, 17:28
Default Re: Implicit boundary conditions
Posts: n/a
In explicit schemes, dependent variables are computed one after another and then the boundary conditions are applied.

Implicit schemes do not give explicit expressions are dependent variables at each grid point. They produce linear (algebraic) equations that relate a dependent variable(s) at a grid point to the dependent variable(s) at other grid points. There are two types of linear equations. [1] Linear equations resulting from implicit discretization of the governing equations in the interior of the domain & [2] Linear equations that result from discretization of the boundary conditions.

These linear systems of equations should be solved (together) to simultaneously obtain the values of the dependent variables in the interior of the computational domain and on the boundaries. So, there is no separate boundary condition routine in implicit schemes. If you use the linear equations [1] (obtained as described above) to get the dependent variables in the interior AND THEN use system of equations [2] to obtain boundary values, the scheme may not converge. [1] and [2] should be clubbed together and solved simultaneously.

Hope this helps.
AshwaniAssam likes this.
  Reply With Quote

Old   February 26, 2001, 21:56
Default Re: Implicit boundary conditions
Atit Koonsrisuk
Posts: n/a
Dear sir, Thank you very much for your kind explaination. I am sorry but I don't understand exactly. Could you please give some examples? Thanks.

Atit Koonsrisuk
  Reply With Quote

Old   February 27, 2001, 13:36
Default Re: Implicit boundary conditions
Posts: n/a
Here is a simple example of a 1-D diffusion problem with an implicit scheme/B.C.

u_t = u_xx ( "-" denote derivatives).

You need an initial condition and two boundary conditions for this problem.

Initial condition : u(t=0,x) = uo(x)

Boundary conditions : i) u(t,x=0) = 0 at x=0 (Dirchlet BC)

ii) u_x(t,x=0) = 0 at x=1 (Neumann BC)

Implicit scheme: "n+1" : new time step values

"n" : old time step values

"i" : spatial location.

Let spatial discretization be done on a grid with spacing = 1 (i.e. Dx = 1).

Discrete first order backward Euler implicit equation:

a){u(n+1,i) - u(n,i)}/dt = {u(n+1,i+1)-2u(n+1,i)+u(n+1,i-1)}

Discrete BC : i) u(n+1,0) = 0

ii) u(n+1,imax+1) = u(n+1,imax) (first order one-sided approximation for the spatial derivative = 0, which is a discrete Nuemann BC).

When you solve the equations by inverting a matrix, you have "imax" number of equations resulting from the discretization of the equations at all interior points (as shown in (a) above) AND two discrete equations that give you the boundary values as shown in (i) and (ii) above.

You have "imax" number of interior points, 2 boundary points. (a) gives you "imax" equations and (i) & (ii) give you two more equations. So you can find the values of u(n+1,i) for all "i" from 0 to "imax+1".

You have to solve (a) and (i) & (ii) simultaneously. If you solve (a) and then (i) & (ii), and then go back to (a) and iterate, the scheme will not converge.

Hope this helps.

  Reply With Quote


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
Boundary conditions for 2D Navie-Stockes simulation L1011 OpenFOAM 5 December 13, 2012 09:17
Proper Pressure Boundary Conditions for Buoyant Flow mchurchf OpenFOAM 0 March 25, 2010 13:16
Concentric tube heat exchanger (Air-Water) Young CFX 5 October 6, 2008 23:17
Trimmed cell and embedded refinement mesh conversion issues michele OpenFOAM Other Meshers: ICEM, Star, Ansys, Pointwise, GridPro, Ansa, ... 2 July 15, 2005 04:15
Please help with flow around car modelling! Tudor Miron CFX 17 March 19, 2004 20:23

All times are GMT -4. The time now is 19:25.