FDTD in Cylindrical Coordinates

[alperuslu]

Hi everyone,

I am dealing with 2D FDTD simulation in Cylindrical coordinate system. I attached my matlab code but there is some problem which i dont undersand. It seems as dispersion but time and space increments obey Caurant stability condition.

Can someone post me FDTD code in Cylindrical coordinates or help me about the problem.


Thanks,
Alper

 

[nasr]

Hi Alperuslu,

What I understand from your code is that your code is 2D code for a cylinder and you create a wave from space position 100,100 :
1-When you defined delr and defined delphi you defined 2 different values for dimensions so you should care about how to calculate the unified time step for not to contradict courant in any dimension.
2-If I understood your code right then your delt should be calculated by multiplying the radius by delphi to get length of arc and not delr by delphi...you should consider that too...as I understand that delr is just the space increment in r direction and not total radius for every cell...hope you get what I mean

Feel free to ask if I misunderstood...

 

[alperuslu]

Hi nasr , first of all thank you for your interest to my problem.

As u said , this is 2D (r-phi) FDTD simulation problem.

1) I have used the smallest grid size which is around (0,0) point (1,1 point in matlab) for calculation of time step. So i took time step as delr*delphi/(2*c) ( actually sqrt(2) but i used 2 instead of it). For this reason i think the wave can not propagate more than 1 cell in a delt even the arc length increases with r and phi. Am i wrong to take time step as constant?

2) I have used delphi*200*delr for time step but again stability problem occurs.

Do you have any FDTD code for cylindrical coordinates? If you have can you send me ?

Thanks ,
Alper

 

[nasr]

Does the arc length increase with r? This is the point which I object about as what you get in the line(delr*delphi) is not the arclength except for the innermost ring of variables only...when you increase the radius (i.e. calculate at a further ring from the center point) the arc length should increase automatically...this doesn't happen in your code that's why I ask you about what you mean by delr?
The other point have 2 solutions, If we will take constant S (Courant stability factor) then we should make for every single ring as we advance in r direction a different delt (That's for phi direction propagation) all S should be the same and one different delt for r direction propagation...Another solution is to use same time step and same S but use the one which guarantees stability but take care that this is a trade of with the simulation speed...

About the cylindrical codes Unfortunately I don't have any...Hope I could help

Nasr