A multiphase cubic MARS method for fourth- and higher-order interface tracking of two or more materials with arbitrary topology and geometry
This addresses challenges in simulating fluid dynamics or material interactions for researchers in computational physics or engineering, though it appears incremental as an extension of existing MARS methods.
The paper tackles the problem of interface tracking for multiple materials with complex topologies by proposing a multiphase cubic MARS method, achieving fourth- to eighth-order accuracy in time and space as demonstrated in benchmark tests.
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.