A multiphase cubic MARS method for fourth- and higher-order interface tracking of two or more materials with arbitrary topology and geometry

TL;DR

This paper introduces a multiphase cubic MARS method for accurately tracking complex interfaces among multiple materials in 2D, with high-order accuracy and adaptive marker distribution.

Contribution

It presents a novel multiphase cubic MARS approach that handles arbitrary topology and geometry with high accuracy and efficiency, surpassing existing methods.

Findings

Achieves fourth-, sixth-, and eighth-order accuracy in space and time.

Handles all types of junctions with ease, unlike VOF and level-set methods.

Demonstrates superior accuracy, efficiency, and versatility in benchmark tests.

Abstract

For interface tracking of an arbitrary number of materials in two dimensions, we propose a multiphase cubic MARS method that (a) represents the topology and geometry of the interface via graphs, cycles, and cubic splines, (b) applies to any number of materials with arbitrarily complex topology and geometry, (c) maintains an $(r,h)$-regularity of the interface so that the distance between any pair of adjacent markers is within a user-specified range, (d) distributes the markers adaptively along the interface so that arcs with high curvature are resolved by densely populated markers, and (e) achieves fourth-, sixth-, and eighth-order accuracy both in time and in space.} In particular, all possible types of junctions, which pose challenges to VOF methods and level-set methods, are handled with ease. Results of a variety of benchmark tests confirm the analysis and demonstrate the superior accuracy, efficiency, and versatility of the proposed method.