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June 28, 2012, 09:34 
about the implemention of periodic boundary condition

#1 
Member

Hi,
I currently meet some problems with the implementaion of the periodic boundary condition for transient RayleighBenard convection problem. My code is based on FVM, SIMPLE algorithm and colocatted grid system (with RhieChow interpolation) . i am prettly sure that my code works for adiabtic boundary condition for temperature (noslip wall for velocities), as i compared my results with some beachmark solutions. To simulate a infinite long domain in horizontal direction (my solver is two  dimensional), i want to implment periodic boundary condition for temperature, velocity and pressure fields. Thus i did some modification of the code, for tempearture and velocity field, i exchange the values on boundaries, like (a N by N grid ) phi(1, j) = phi(N1,j) phi(N,j) = phi(2,j) then treat the boundary type like Dirichlet condition; for pressure field, at the beginning i think we may not need any modification as the problem i considered is not like the other type periodic boundary condition , like there is a incomming flow and we need to guarantee the constant pressure drop. then i realized that the pressure correction genearlly implicitly incoperates with Neumann boundaries for all boundaries, then i did some modification like temperature field. However, i failed, as the solver directly divergence in the first two or three time steps and i do not know the reason. I wish someone who has similar experience can help me. If someone can provide some usful materials, it would be great. 

June 28, 2012, 09:36 

#2 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,417
Rep Power: 31 
you have to change your matrix by means of the link in the periodicity, you cannot use Dirichlet BCs..


June 28, 2012, 09:50 

#3 
Member

do you mean for the pressure correction equation?
in each time step, i firstly compute U, V then compute P finally compute T in the subroutine for computing pressure correction, i first assemble AE, AW, AN, AS, AP and right hand side (Su) then i set the value on boundaries according to the periodic boundary conditions, take the west side as example, i set pp(1,j) = pp(N1,j) , pp stands for pressure correction; since i have the values on boundaries, i treat it like Dirichlet boundary condition then i call the linear sysmeter solver ... This is the procedure i did, do you mean 'even i known the values on boundaris , i can not treat it like Dirichlet type'? so what should i do ? Thank you for your quick reply. 

June 28, 2012, 16:55 

#4 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,417
Rep Power: 31 
Example:
at point i=2 (p(i1,j)  2*p(i,j) + p(i+1,j))/dx/dx becomes (p(N1,j)  2*p(i,j) + p(i+1,j))/dx/dx that means you changed the position in to the matrix entry. You never compute the value p(1,j) until the pressure solver has converged 

June 28, 2012, 17:31 

#5 
Member

I get your point, in fact, i asked my teacher this afternoon, he shared a similiar idea ...
though i unstand your meaning now, there seems to be some problem from the implementaion point of view. it seems this problem will change the structure of the coefficinet matrix to be nondiagonal ... which means tranditional linear system solver (like SIP ) may fail tomorrow i will try to add one or two layer of ghost cells to see it works or not ... thank you for your reply again .... 

July 12, 2012, 04:30 

#6 
Member
Ren/Xingyue
Join Date: Jan 2010
Location: Nagoya , Japan
Posts: 44
Rep Power: 8 
hi, dear harbinyg,
I faced same problem when I try to solve Poisson equation in cylindrical coordinates. And I didn't use any boundary condition in that case. An*pn=Aw*p1+...+bn A1*p1=Ae*pn+.. +b1 Just treat the points beside the periodic boundary as internal points, and that can solve the problem implicitly. 

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