[lamare]

Hi all,

I am investigating whether or not I could use OpenFoam to simulate an aether based model for Electromagnetics, whereby I model the aether as an ideal compressible fluid, whereby the Laplacian is used to define a scalar electric potential Phi, a vector magnetic potential A, a vector field E for the electric field and a vector field B for the magnetic field.

You see, historically, Maxwell started out with a very simple model: the aether is like a fluid. He used that analogy to describe the magnetic and electric fields, but the connection to the underlying model was lost and with it the terms which describe the compressibility of the aether.

When you re-start from scratch and model the aether as an ideal compressible fluid and use the Laplace operator, you can re-define both fields in a simple and straightforward manner. I will use [] to denote a vector. Sorry for not using Tex, I can't find how to do this on the forum.

Field definition:

The basic continuous fluid model uses the velocity within the fluid for describing waves, vortices, etc. The Laplace operator gives you the 2nd derivative of the velocity field with respect to position [x]:

Nabla^2 = grad div [v] + rot rot [v].

Notice there are two terms, both computed in two steps, so we get 4 in between variables, when implemented in software, or "fields" in math language. We just give these the familiar names, and that's it:

Electric potential:
Phi = div [v]. [/s] or [Hz].

Magnetic potential:
[A] = rot[v]. [radians/s]

Since rot div[v]=0 and grad rot[v]=0 as well, we now have a divergence free component in the magnetic potential and a rotation free component in the electric potential.

The next step is to take the gradient of the electric potential, which gives you the electric field [E]:

[E] = grad(Phi) = grad div [v]. [/(ms)] or [Hz/m]

And to take the rotation of the magnetic potential, which gives you the magnetic field [B]:

[ B ] = rot[A] = rot rot [v].

This *must* also have a unit of measurement of [/(ms)] or [Hz/m], otherwise the two components of the Laplacian wouldn't add up.

Added together, we get the Laplacian, of course:
Nabla^2 = [E] + [ B ] = grad div [v] + rot rot [v].

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So, that's my field definition. Just an ideal compressible fluid, whereby only the parameters (density, etc..) have different values as they would be when modelling acoustics or hydrodynamic flows and/or waves within an ideal compressible fluid.

So, my question comes down to:

Can I simulate both the vorticity c.q. rotational flows of the compressible fluid (magnetic field, rot rot[v]) as well as the compressible flow (electric field, grad div [v]) at the same time to study, for example, the radiation pattern of an antenna?

In this model, this would involve the radiation of vortex rings as well as longitudinal compression waves....

If yes, can you give me any directions on how/where to start?

Thanks,

Arend Lammertink.