Problem with Joule-Heating simulation in a high aspect-ratio system
 

Hello,

I have a problem with a code which I have written to simulate Joule-Heating through a 3D cubic system made of silver. When the aspect ratio between l_x/l_y (l_x and l_y are the length of the system in x and y direction) is less than 100, I get good results from the code independent of the number of grid points generated in the system. However, when the l_x/l_y is larger than 100, the temperature distribution predicted by the model shows deviations from a true symmetric distribution for even 30000 grid points which are not really large. What could be the problem? I have used a resistive networks to solve electrical and heat conduction equations.

I appreciate for any help.

Farshad

Hi Farshad,

• Are you using a CFD package, and if so - which?
• With a large aspect ratio, did you also use high aspect ration cells? If so - it can explain the difficultiy you are experiencing.
• You did not mention the Lz / Lx ratio. Please specify.

Hi Rami,

Thanks for your answer. I am using our in-house code which is basically a Finite-Difference code. I think you are right. Because I try to shrink the aspect ratio of the grids in the high-aspect ratio case and now it's giving me the right answer. Lz/Lx = 1.

Thanks again,

Farshad

Rami,

Is there any mathematical rule or basis for choosing the correct value for the time step as well as grid boxes for large geometrical aspect ratio?

Farshad

The time step should be selected by considering stability and accuracy. The stability depends on the scheme you use, and - if your boundary conditions, initial conditions and sources are extremely time- or space- dependent (e.g., have discontinuities of high derivatives) - they may also influence stability. Accuracy is usually improved by smaller time-steps. The aspect ratio is implicitly dealt with when considering the characteristic length for stability.