Numerical modelling of non‐linear coupled thermo‐electric problems

Igor O. Golosnoy (School of Electronics and Computer Science, University of Southampton, Southampton, UK)
Jan K. Sykulski (School of Electronics and Computer Science, University of Southampton, Southampton, UK)



The purpose of this paper is to access performance of existing computational techniques to model strongly non‐linear coupled thermo‐electric problems.


A thermistor is studied as an example of a strongly non‐linear diffusion problem. The temperature field and the current flow in the device are mutually coupled via ohmic heating and very rapid variations of electric conductivity with temperature and applied electric field, which makes the problem an ideal test case for the computational techniques. The finite volume fully coupled and fractional steps (splitting) approaches on a fixed computational grid are compared with a fully coupled front‐fixing method. The algorithms' input parameters are verified by comparison with published experiments.


It was found that fully coupled methods are more effective for non‐linear diffusion problems. The front fixing provides additional improvements in terms of accuracy and computational cost.


This paper for the first time compares in detail advantages and implementation complications of each method being applied to the coupled thermo‐electric problems. Particular attention is paid to conservation properties of the algorithms and accurate solutions in the transition region with rapid changes in material properties.



Golosnoy, I. and Sykulski, J. (2009), "Numerical modelling of non‐linear coupled thermo‐electric problems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 3, pp. 639-655.

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