A versatile interface model for thermal conduction phenomena and its numerical implementation by XFEM

A general interface model is presented for thermal conduction and characterized by two jump relations. The first one expresses that the temperature jump across an interface is proportional to the interfacial average of the normal heat flux while the second one states that the normal heat flux jump is proportional to the surface Laplacian of the interfacial average of the temperature. By varying the two scalar proportionality parameters, not only the Kapitza resistance and highly conducting interface models can be retrieved but also all the intermediate cases can be covered. The general interface model is numerically implemented by constructing its weak form and by using the level-set method and XFEM. The resulting numerical procedure, whose accuracy and robustness are thoroughly tested and discussed with the help of a benchmark problem, is shown to be efficient for solving the problem of thermal conduction in particulate composites with various imperfect interfaces.