[abhi084]

Can anybody explain or provide a program for solving unsteady diffusion equation in 3D for cylindrical coordinates. I mean I am trying solving using FVM (with uniform grid distribution from r=0 to r=R) method but am not sure how to apply the symmetry BC at the axis i..e dt/dr=0 (these are partial derivatives) i.e at r=0.

If anybody has written the program in cylindrical coordinates please help me.

[FMDenaro]

In a FV method, the axis r=0 cannot be the locus of the faces of a cell.
You can construct the method by starting from the integral form and using the first face of the cell at r=dr/2.

[abhi084]

first cell face at dr/2. ok so u mean keep first Boundary at dr/2 an d have a node at centre of this cell or keep one face at dr/2 and have the node at axis?

[FMDenaro]

Originally Posted by abhi084

first cell face at dr/2. ok so u mean keep first Boundary at dr/2 an d have a node at centre of this cell or keep one face at dr/2 and have the node at axis?

you can set the node at the axis r=0 and the face at r=+dr/2. For symmetry you have the condition at r=-dr/2. This way, you can compute the balance from the fluxes and have the update for the nodes along r=0.
Remember to use the integral form, not the differential one.




|........ o........ |.......... o............ |.... o.... |

-dr/2.. r=0 ...+dr/2....r=dr....... +3dr/2

[abhi084]

Originally Posted by FMDenaro

you can set the node at the axis r=0 and the face at r=+dr/2. For symmetry you have the condition at r=-dr/2. This way, you can compute the balance from the fluxes and have the update for the nodes along r=0.
Remember to use the integral form, not the differential one.




|........ o........ |.......... o............ |.... o.... |

-dr/2.. r=0 ...+dr/2....r=dr....... +3dr/2

Okay yeah thanks was thinking along the same line. Now just one more query, since it is like a 3D problem with r,theta,z let us say that temp matrix is T(i,j,k). Let us say i is for r, j for theta and k for z. But at r=0 how can we have a matrix of the form T(i,j,k) since there is no theta over there. How to take care of this...? (like t(i,j,k) is okay for everywhere else but wat about at r=0 that is main problem)

[FMDenaro]

you get r=0 for i=1 and the plane (1,j,k) of the matrix contains value depending only on the k index (z direction).

[abhi084]

Originally Posted by FMDenaro

you get r=0 for i=1 and the plane (1,j,k) of the matrix contains value depending only on the k index (z direction).

Okay thanks......will see to it.......was getting confused here only.....thanks.....but do you have any code of this type by any chance....any programming language would do......