Dislocation transport using an explicit Galerkin-Least Squares formulation
Résumé
An explicit Galerkin/least squares formulation is introduced for a quasilinear transport equation in Field Dislocation Mechanics (FDM) and applied to the study of the kinematics of dislocation density evolution in the following physical contexts: annihilation of dislocations, expansion of a dislocation loop, simulation of Frank-Read sources. This conditionnaly stable method leads to a symmetric well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. The weak solutions to these equations are not unique, and the method is able to capture shock formation as well as rarefraction waves by appropriate algorithmic modifications.