Numerical model of simple magnetic circuit

[LastCharge]

Homework Statement

I have to build a 2D model of simple magnetic circuit, that is iron core (2) with coil(1) and air gap(3) applied to it. Model has to be solved on numerical basis, by finite difference or element method (whichever is easier to implement). Number 4 on drawing represents boundary condition, that would be magnitude of magnetic field density B = 0.

http://img813.imageshack.us/img813/4049/trafon.th.jpg

Homework Equations

What equations to use and how properly discretize them?

The Attempt at a Solution

I started with differential form of Ampere law, which is:
curl(H) = J, where H is vector of magnetic field strength and J is vector of current density.
Because B has only 2 space components (third iz zero), curl(H) translates to:
(dHy/dx - dHx/dy) *ez = J * ez, where Hy is y component of H, Hx is x component of H and ez is the direction in z-axis.
ez falls out, so final form is:
dHy/dx -dHx/dy = J

First derivatives are substituted with differences, i'll use central difference approximation:
du/dx = (u_(i+1) - u_(i-1))/(2*deltax)

Hy_(i+1,j) - Hy_(i-1,j) - Hx_(i,j+1) + Hx_{(i ,j-1)} = J*2*deltah
Grid is equidistant, so for both dimensions deltah is same.

I used the formula above for the coil region, elsewhere I set equation to (where no current density):
Hy_(i+1,j) - Hy_(i-1,j) - Hx_(i,j+1) + Hx_{(i ,j-1)} = 0

I got some strange and most possible, wrong results.

thank you in advance

 

[mark726]

for any help or advice.

Hello,

Thank you for sharing your progress so far. It seems like you have a good understanding of the equations involved in this problem. To properly discretize them, you will need to choose a suitable grid size and time step. This will depend on the specific parameters of your model and the accuracy required for your results.

Once you have chosen your grid size and time step, you can use the central difference approximation for the first derivatives as you have done. However, for the boundary condition at point 4, you will need to set the value of B to zero, not just the equation. This can be done by setting the value of H to zero at that point.

It is also important to make sure that your boundary conditions are consistent with the equations you are using. For example, if you are using the differential form of Ampere's law, then your boundary conditions should involve the magnetic field strength H, not the magnetic field density B.

I would suggest reviewing your boundary conditions and making sure they are consistent with the equations you are using. Also, double check your implementation of the central difference approximation to make sure it is correct.

I hope this helps and good luck with your model!