Numerical treatment of rapidly changing and discontinuous conductivities

The Kirchhoff transformation is an effective means for dealing with temperature dependent conductivities. In general numerical applications, however, the use of this approach will produce non-linear discrete equations, which can be costly to solve. This paper introduces a local Kirchhoff approach for approximating the conductivity terms in the discrete equation. This approach results in an efficient solution in terms of temperature alone. Application to a problem with rapidly changing conductivity shows that use of high-order numerical integration in the conductivity approximation leads to very accurate predictions.