
[Sponsors] 
Poisson equation: nonsymmetric matrix with nonuniform spacing? 

LinkBack  Thread Tools  Display Modes 
July 25, 2012, 03:22 
Poisson equation: nonsymmetric matrix with nonuniform spacing?

#1 
New Member
Daniel Weber
Join Date: Nov 2009
Posts: 4
Rep Power: 9 
Hello,
I'm trying solve a poisson equation with finite differences. According to "Computational Methods for Fluid Dynamics" the finite difference approximation of the laplace operator in the 1D poisson equation is p_i+1 (xi  x_i1) + p_i1(x_i+1  x_i)  p_i (x_i+1  x_i) / [ 1/2 * (x_i+1  x_i1) * (x_i+1  x_i ) * ( x_i  x_i1) ] If the grid spacing is uniform the matrix is symmetric, but not for nonuniform grid spacing. With nonuniformity the requirements is that the distance between each pair of odd and even unknowns (x_i  x_i+2, x_i+1  x_i+3) must be equal. I could artificially move the unknows a bit, but generally that limits the transformation function of the grid. I would like to use a CG method, so is there anything I can do modify the scheme. (or maybe use finite volumes?) How is the pressure correction done in Finite Volume methods? Are the matrices as well nonsymmetric? Any hint or a pointer to literature would be very helpful! Thank you! Daniel 

July 25, 2012, 03:54 

#2  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,075
Rep Power: 35 
Quote:
Yes, on nonuniform grids the matrix is symmetric in its shape but not in the entry values 

July 25, 2012, 08:21 

#3  
Member
G. S.
Join Date: Nov 2010
Posts: 53
Rep Power: 8 
Quote:
Best regards... 

July 26, 2012, 03:03 

#4 
Senior Member
Arjun
Join Date: Mar 2009
Location: Nurenberg, Germany
Posts: 624
Rep Power: 19 
Poisson operator should give you symmetric matrix ie
Aij = Aji It is true in case of non uniform meshes too. 

July 26, 2012, 03:10 

#5 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,075
Rep Power: 35 

July 26, 2012, 05:52 

#6 
Senior Member
Arjun
Join Date: Mar 2009
Location: Nurenberg, Germany
Posts: 624
Rep Power: 19 

July 26, 2012, 11:16 

#7 
New Member
Daniel Weber
Join Date: Nov 2009
Posts: 4
Rep Power: 9 
Hi,
thanks for the answers. Yes, I meant nonsymmetric in the values. But I'm still curios if there are as well nonsymmetric matrices(in the values) when I use a finite volume discretization for the pressure correction. Does anybody have i hint? best regards, Daniel 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Free jet simulation  msarkar  OpenFOAM Running, Solving & CFD  35  February 21, 2017 19:36 
fluentMeshToFoam multidomain mesh conversion problem  Attesz  OpenFOAM Other Meshers: ICEM, Star, Ansys, Pointwise, GridPro, Ansa, ...  12  May 2, 2013 10:52 
buoyantSimpleFoam divergence  TomS  OpenFOAM Running, Solving & CFD  0  November 24, 2011 15:16 
Neumann Boundary Condition for Poisson Equation solution in Polar Coordinates  prapanj  Main CFD Forum  2  July 30, 2011 19:07 
Problem with Poisson equation with Neumann BC  Jeff67  Main CFD Forum  0  March 27, 2011 11:23 