# Mesh of solid conductor with skin effect

## Mesh of skin depth: rules to follow

To obtain accurate results in skin effect problems (eddy currents, etc.), at least two elements should be used on the skin depth.

The state variable actually has an exponential variation on the skin depth, but within an element, Flux 2D uses a parabolic approximation. Thus, the size of elements should be small enough that the arc of parabola can be assimilated to an exponential arc.

## Computation of skin depth: recall

In magneto-harmonic problems with linear materials, the skin depth for eddy currents can be expressed as follows:

where f is the frequency, ρ the resistivity and μ the magnetic permeability.

## Choosing the mesh generator

To mesh the skin depth , elements of rectangular or hexahedral type are recommended, that is:

- the mapped mesh generator (2D, 3D)
- an extruded mesh generator with a mapped base (3D)

The rest of the study domain is meshed using the automatic mesh generator.

## 2D Example

A 2D example of mesh on the skin depth is shown in the figure below.

## 3D Example

A 3D example of mesh on the skin depth is shown in the figure below.

The most critical volumes (the volumes corresponding to the skin depth of the bar) are meshed using the extrusive mesh generator. The rest of the study domain is meshed using the automatic mesh generator (inside the bar and the surrounding air).