sweep problem
 

Dear friends,

Solving a 2D (axial symetrical cylindrical geometry) unsteady heat conduction prob using a finite differences scheme, I am using TDMA as a solver. I noticed that if I use it in axial direction the solution is very fast. However if I use TDMA in radial direction, the solution obtained takes time and is almost 7 times longer to get than in axial direction. I think the main reason is due to the boundary conditions existing in those directions, since in axial direction both boundaries are at constant temperature. However such usfull information doesn't exist in radial direction. This order of selection is called by Patankar "the sweep". Is it true or I am wrong and there is another reason due to a serious problem in my program itself ???

Thank you for your contributions

Re: sweep problem
 

(1). I think the convergence rate depends on many factors, the initial flow field guess, the goemetry, the boundary conditions and the mesh. (2). For your problem, you can switch the boundary conditions and check out your theory, to see whether it is always converges faster in a particular sweep direction. (3). And it is obvious that if the problem is nearly 1-D then the solution would converge faster in the 1-D direction, because the solution in the normal direction would be nearly uniform.

Re: sweep problem
 

Patankar has very well described this in his book.The TDMA traverse direction (sweep direction) should be selected from the geometry with the bcs.Please remember that TDMA sends the bc info immediately into the interior(local 1D)and its traverse transmits the bc @one point per sweep.