Here is a presentation of the Flux environment; the project management, the data management, the command language, the
formulas and mathematical functions.

The construction of a Flux project consists of several stages: Geometry → Mesh → Physics → Resolution → Postprocessing;
with the possibility to import a CAD file, a mesh, materials...

Flux PEEC is a 3D modeling module dedicated to electrical interconnections of power electronics devices. It also
provides RLC extraction and generation of SPICE-like equivalent circuits.

Flux provides a unified Material Identification tool based on the Altair Compose environment allowing to run an identification
of the coefficients required to create material in Flux.

This documentation deals with the Jython script used in Flux and allows to understand the various structures of
entities and functions, and use it in user scripts for example.

This example shows the advantages of the integral method compared to the conventional
finite element approach for a current sensor. In this case, a current is injected
into the main conductor and we are looking to compute the magnetic flux observed by
the auxiliary coils, as shown in Figure 1.
The characterization of this sensor requires knowledge of its gain and
crosstalk.

This device being characterized by a large quantity of leakage flux and by the
distances between the conductors that can be large, the use of the conventional
finite element method requires to intensively mesh the surrounding air. To get
results approaching the real the solution, the mesh must be symmetrical and very
dense, which increases the computation time (see Figure 2).
The integral method is much cheaper in terms of meshing elements because we do
not mesh the air anymore (see Figure 3).

Comparison of the two methods:

Table 1. Computation time for one value of current in the main conductor

Method

Mesh

Solving

Flux computation

Integral

2s

30s

1s

Finite elements

20min

5min

20min

For the computation of the flux in a coil, the volume integral method is
also faster than the finite element method. This magnetic flux is split into two
contributions, the contribution of the other coils and the contribution of the
magnetic parts [2]. In the air and for the other coils we compute the magnetic flux
by a Biot & Savart law. For the magnetic parts the computation is done with the
magnetic vector potential already computed in resolution.

Results

The study of this sensor requires to know its gain defined in the frequency domain by
the following relation:
${G}_{0}=\frac{2\pi \phi f}{{I}_{0}}$
with

f : the frequency

${I}_{0}$
: the current in the main conductor

$\phi $
: the magnetic flux in the auxiliary coils

We can compute the gain for several values of current :
Figure 4 shows that the finer the mesh is, the more the results will be
close to the real solution and therefore to the solution provided by the integral
method.

A complete study also requires knowing the crosstalk of the sensor,
$\lambda =\left|\frac{G}{{G}_{0}}\right|$
with,

G : the gain corresponding to the sensor with an offset on the position of
the main conductor.

Note: Total simulation time with the integral method for this study: 15 minutes.

Note: Total simulation time with finite element method with dense mesh for this study: 6
hours

References

[2] : L. Huang, G. Meunier et al., “General Integral Formulation of Magnetic Flux
Computation and Its Application to Inductive Power Transfer System,” IEEE Trans. on
Mag., vol. 53, no. 6, pp. 1-4, June 2017.