A linear MARS method for three-dimensional interface tracking

TL;DR

This paper introduces a linear MARS method for explicit 3D interface tracking that maintains mesh regularity, preserves topology, and achieves high accuracy, demonstrated through benchmark tests.

Contribution

The paper presents a novel linear MARS approach that handles complex 3D interfaces with high accuracy and mesh regularity, improving upon existing methods.

Findings

Effective mesh adjustment algorithms enforce regularity.

High accuracy demonstrated in benchmark tests.

Method preserves topology and geometric features.

Abstract

For explicit interface tracking in three dimensions, we propose a linear MARS method that (a) represents the interface by a partially ordered set of glued surfaces and approximates each glued surface with a triangular mesh, (b) maintains an $(r,h,\theta)$-regularity on each triangular mesh so that the distance between any pair of adjacent markers is within the range $[rh,h]$ and no angle in any triangle is less than $\theta$, (c) applies to three-dimensional continua with arbitrarily complex topology and geometry, (d) preserves topological structures and geometric features of moving phases under diffeomorphic and isometric flow maps, and (e) achieves second-order and third-order accuracy in terms of the Lagrangian and Eulerian length scales, respectively. Results of classic benchmark tests verify the effectiveness of the novel mesh adjustment algorithms in enforcing the $(r,h,\theta)$-regularity and demonstrate the high accuracy and efficiency of the proposed linear MARS method.