Improving the accuracy of FEM simulations of time-domain inductive sensors through separation of secondary field effects

FEM simulation is commonly used to predict the behaviour of, and inform design choices for, electromagnetic sensing systems. The main purpose of such simulations is to determine the secondary fields produced by conductive targets in response to incident primary field generated by a sensor. In the multi-physics engine COMSOL the magnetic fields interface does not directly distinguish between primary and secondary fields, solving for full field only. In order to determine the secondary voltage induced in a sensing coil a secondary study is required to establish the components making up primary and secondary effects. In some cases it is possible to use a vacuum, or air-only case where no inductive medium is present to isolate only the coil coupling by subtraction. In the case of seawater detection, as a means to determine sea ice thickness, the resultant secondary effect can be on the scale of 0.7% of the full field values, and so may be on a similar scale to the noise within the simulation. This paper presents an approach making use of the ‘withsol()’ operator as a pointer to a partial solution from the full field simulation; specifically the time varying X, Y and Z components of current density in the subject inductive medium, and using these as inputs for a ‘secondary effects only’ simulation. This method splits the problem, therefore removing the need for subtraction, which may reduce the effect of errors. This approach has been shown to produce simulated secondary voltages whose RMSE to an equivalent experimental data set was 3.3% over a period of 189 µs. This value drops to 2.8% if the 0.2 m and 0.4 m are discounted, as these heights experienced sensor saturation. The method presented in this paper can also be applied to mitigate similar mesh subtraction-based errors in simulation of multi-coil inductive sensing systems.