Non-meshed coil magnetic sources


This chapter discusses the creation of non-meshed coils in a Flux project. Differently from meshed coil regions, this type of coil entity is a special case of non-meshed magnetic source.

The following topics are covered in this documentation:
  • What this type of non-meshed magnetic source models.
  • How to create a non-meshed coil in a Flux project.
  • Limitations.
  • Example of application.

What this type of region models

A non-meshed coil may be interpreted as a current path in three-dimensional space that generates a magnetic field accordingly to the Biot-Savart law. Non-meshed coils do not belong to the finite element domain represented in a Flux project in the usual sense. They should be regarded instead as being superposed to the domain, since they are independent from discretizable geometrical entities such as lines, faces and volumes.

Non-meshed coils are not linked to physical regions either, diversely from meshed coil entities that are also available in Flux. On the other hand, a non-meshed coil must be connected to an external circuit or have its current imposed in way similar to a meshed coil region, i.e., by means of a FE coupling component.

Due to the characteristics described above, a non-meshed coil may be included in a Flux project without further complexifying the geometry or the finite element mesh. Thus, the non-meshed coil approach is useful for the representation of devices exhibiting complicated geometries, or when the winding itself has an elaborate shape.

The following winding types may be promptly represented in a Flux project with a non-meshed coil magnetic source:
  • circular coil;
  • rectangular coil;
  • saddle coil and multi saddle coil.

Moreover, coils with an arbitrary shape may be represented with the following non-meshed coil type

  • Composed coil.

How to create it in a Flux project

The user may start creating a non-meshed coil before or after meshing the geometry in any of the two following ways:
  • by choosing New in menu PhysicsNon-meshed coil.
  • or by clicking twice on Non-meshed coil in the Data tree, under PhysicsNon-meshed magnetic sources.

In both cases, Flux displays a window dedicated to the creation of a new non-meshed coil.

To proceed, in the Geometric Definition tab, the user must:

  • Select a coil template from the Type of coil drop down menu.
  • Provide the geometrical parameters (system of coordinates, dimensions, etc.) required by the selected coil template. Since each template requires a different set of geometrical parameter, the list of inputs and their descriptions in the Geometric Definition tab change to conform to the chosen template.
    Note: The existing coil templates correspond to the coil types mentioned in previous section. A synthetical outline of the geometrical parameters defining each coil type is available in this documentation topic. For a detailed discussion on each coil template, please refer to the links below:
    Note: The coil creation window also contains an animated figure that further clarifies the meaning of each geometric parameter of the selected coil template.
    Note: To model simple shapes, the user is invited to use only the predefined shapes (such as the Circular coils, Rectangular coils, Multi saddle coils, Saddle coils) according to the design of the coil. Using the Composed coil the results may differ as the decomposition in elementary beams may not be the same. The user is invited to fill the Curvature radius to compare properly the Composed coil to the other predefined shapes.

In the Electrical tab, the following parameters must be provided:

  • The electric component (stranded coil) associated with the coil;
  • The number of turns;
  • The coil fill factor (optional);
  • The resistivity of the coil material in Ω.m (optional);
  • The coil material density in kg/m3 (optional).
Still in the Electrical tab, the user must also specify the behavior of the non-meshed coil with respect to symmetries or periodicities. More specifically, the two following fields must be set:
  • Symmetries and periodicities: conductors in series or parallel
  • Symmetries and periodicities: duplication or none
    Note: In projects that do not contain any periodicities or symmetries, the user may leave both of these fields unchanged (that is, set to their default options : All the symmetrical and periodical conductors are in series and Duplication by the symmetries and the periodicities, respectively).
    Note: For further information on adjusting these fields in projects containing a symmetry or a periodicity, please refer to the documentation topic discussing how symmetries and periodicities affect the creation of coil entities in Flux.


Non-meshed coils are available in all magnetic applications, but only in Flux 3D, as discussed in this documentation topic.

To evaluate the Joule losses dissipated in a non-meshed coil, the user must provide two of the optional parameters mentioned in the previous sections simultaneously. More precisely, both the coil material resistivity and the winding fill factor must be specified in the Electrical tab during the creation of the non-meshed coil, to enable the post-processing of Joule losses and other related quantities (e.g., the evaluation of an equivalent resistance).

If none or only one of those parameters is provided, the post-processing of the Joule losses will exhibit a behavior that is similar to the case of a coil conductor region without losses. In other words, Flux cannot evaluate an equivalent resistance nor the Joule losses without knowledge of those parameters.

On the other hand, if both the resistivity and the fill factor are provided, the post-processing of the Joule losses with a non-meshed coil magnetic source will behave similarly to the case of coil conductor regions with losses an simplified geometrical description. Thus, note that non-meshed coils are unable to represent current concentration phenomena linked to the skin and proximity effects in AC Steady State and in transient applications, underestimating Joule losses at higher frequencies.

Note: In magnetostatic applications, Flux can only evaluate an equivalent resistance of a non-meshed coil. The direct evaluation of Joule losses with sensors or with a computation on a physical entity is not yet available in this kind of application.

The FE coupling component associated to a non-meshed coil may be connected to a coupled electric circuit or have its current imposed. In the former case, and if the project does not contain an infinite box, the user must position the non-meshed coil in a meshed part of the domain to obtain correct results. In the latter case (i.e., FE coupling components with imposed current), the non-meshed coil may be placed anywhere in the domain (including empty, non-meshed regions) even in the absence of an infinite box.

The computation of electromagnetic forces on non-meshed coils is not yet available in Flux. In applications requiring the evaluation of forces on coils, the user should instead employ meshed conductor regions.

Example of application

Figure 1 shows part of the main magnet of a medical MRI scanner that was modeled in Flux 3D with the help of non-meshed coils.

Figure 1. An MRI magnet represented by non-meshed coils in Flux 3D. The axial component of the magnetic flux density was computed in a Magnetostatic application and displayed as a color map on a rectangular cross section of the magnet (b). The high degree of homogeneity of the field is crucial for the generation of good quality images in MRI applications.

In the project above, the Composed coil template available for non-meshed coils was used to represent six subcoils of the MRI magnet. This type of non-meshed coil is particularly useful to represent windings with complex geometries, since it allows the user to import a file containing a list of point coordinates describing the current path in the winding, as in the case of this example.

Using non-meshed coils is advantageous in such situations, because they simplify the description of the geometry in the Flux project. The non-meshed, composed coils are simply superposed to the computational domain and remain independent from the geometry.

An alternative representation of the same MRI device could be created as well with meshed coils. Figure 2 shows the same part of the MRI magnet modeled in Flux 2D in an axisymmetric magnetic application. The winding was represented by coil conductor regions with losses and simplified geometrical description.

Figure 2. Alternative representation of the MRI magnet in Flux 2D using meshed coil regions in an axisymmetric simulation (a). The finite element mesh (b) and the magnetic flux density field lines (c) are also shown.

Table 1 compares the magnetic flux density evaluated with these two models, showing that the result obtained with the non-meshed coil approach is in good agreement with the meshed coil model. In both cases, the MRI magnet was traversed by a current of 1 A and a sensor was employed to evaluate the magnetic flux density at its center.

Table 1. Evaluation of the magnetic flux density with a sensor in the center of the MRI magnet with two different modeling approaches (3D non-meshed coils X 2D axisymmetric meshed coil regions).
Non-meshed coils (Flux 3D) Meshed coil regions (Flux 2D - axisymmetric)
Magnetic flux density at the center of the magnet - axial component (µT) 102.82 102.88