A high-order fully Lagrangian particle level-set method for dynamic surfaces
Abstract
We present a fully Lagrangian particle level-set method based on high-order polynomial regression. This enables closest-point redistancing without requiring a regular Cartesian mesh, relaxing the need for particle-mesh interpolation. Instead, we perform level-set redistancing directly on irregularly distributed particles by polynomial regression in a Newton-Lagrange basis on a set of unisolvent nodes. We demonstrate that the resulting particle closest-point (PCP) redistancing achieves high-order accuracy for 2D and 3D geometries discretized on highly irregular particle distributions and has better robustness against particle distortion than regression in a monomial basis. Further, we show convergence in a classic level-set benchmark case involving ill-conditioned particle distributions, and we present an application to an oscillating droplet simulation in multi-phase flow.
Cite
@article{arxiv.2306.07986,
title = {A high-order fully Lagrangian particle level-set method for dynamic surfaces},
author = {Lennart J. Schulze and Sachin K. T. Veettill and Ivo F. Sbalzarini},
journal= {arXiv preprint arXiv:2306.07986},
year = {2024}
}