A general and efficient computational procedure for modelling the Kapitza thermal resistance based on XFEM

The thermal resistance of an interface between two materials, conceptualized by Kapitza, is an important physical phenomenon encountered in many situations of practical interest. The numerical treatment of this phenomenon has up to now run into difficulties due to the temperature discontinuity. In this work, a general and efficient computational procedure for modelling the Kapitza thermal resistance is proposed, which is based on the extended finite element method (XFEM) in tandem with a level-set method. The steady thermal conduction in a two-phase material with the Kapitza thermal resistance at the interface is first formulated in a variational way and then numerically treated with the proposed computational procedure. Different three-dimensional numerical examples with known analytical solutions show the high accuracy and robustness of the proposed computational procedure in capturing the temperature jump across an interface.