A Lagrangian particle level set method

We present a novel particle level set method for capturing interfaces. The level set equation is solved in a Lagrangian frame using particles that carry the level set information. A key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field. The Lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions. The efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface. The simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments.