This report is a feasibility study of a level-set method for the computation of moving material-void interfaces in an Eulerian formulation. The report briefly introduces level-set methods and focuses on the development of such a method, that does not just accurately resolve the geometry of the interface, but also the physical quantities at and near the interface. Results are presented for illustrative model problems. As concerns its ability to improve the geometrical resolution of free boundaries, as expected, the level-set method performs excellently. Concerning the improvement of physical (all other than merely geometrical) free-boundary properties, the method performs very well for downstream-facing fronts and is promising for upstream-facing ones.
Koren, B., & Venis, A. C. J. (1999). A fed back level-set method for moving material-void interfaces. Journal of Computational and Applied Mathematics, 101(1-2), 131-152. https://doi.org/10.1016/S0377-0427(98)00203-9