On the simulation of a moving discontinuity by boundary element methods

Abstract

The movement of a discontinuity in a continuum can usually be expressed in terms of the state in its direct vicinity. Thus, the knowledge of the local state around the discontinuity is vitally important in order to adequately describe its movement. Numerical schemes local to the discontinuity, as e.g. moving finite element methods, are appropriate approaches to describe its motion. However, for a large number of problems, the local state not only depends on measures of the discontinuity plane itself but also on measures related to the bulk behavior of the material, such as temperature or stress. For a complete description, the bulk behavior of the material has to be numerically modeled as well. In this contribution, the interface and its propagation is modeled explicitly by a two-dimensional discretization of the interface. The same discretization is utilized to describe the behavior of the bulk material employing the boundary element method. As an example, the movement of a phase transition front in a single crystal is presented.