Design of a high-order front tracking method in 2D

This document presents a proposal for a new high-order front tracking method in 2D. A thorough review of existing methods for moving and/or irregular boundaries is presented. From this review, the 1D front-tracking approach of Gatti-Bono emerges as the most promising starting point for a higher-dimensional method. The Gatti-Bono method in 1D is then explained in detail, and a 2D extension is proposed. This extension incorporates a number of ideas from the literature on embedded boundary methods for stationary irregular geometries.