A new method for interface tracking is presented. The interface representation, based on domain decomposition, provides the interface location explicitly, yet is Eulerian. This allows for well established finite difference methods on uniform grids to be used for the numerics of advecting the interface and other computations. CFL-stable and second order accurate explicit and implicit time-stepping methods are derived. Numerical results are given to substantiate stated convergence properties, as well as convergence in interface curvature and mass conservation. Our method is applied to a boundary integral formulation for Stokes flow, and the resulting integrals are analyzed and treated numerically to second order accuracy. Finally, we embed our method in the familiar immersed boundary- and immersed interface methods for two-phase Navier-Stokes flow.
Boundary-Conforming Free-Surface Flow Computations: Interface Tracking for Linear, Higher-Order and Isogeometric Finite Elements
RWTH Aachen University（亚琛工业大学）；Chair for Computational Analysis of Technical Systems (CATS)（技术系统计算分析讲席）；Center for Computational Engineering Science (CCES)（计算工程科学中心）
A variational front-tracking method for multiphase flow with triple junctions
Fakultät für Mathematik, Universität Regensburg（雷根斯堡大学数学学院）；Dipartimento di Mathematica, Università di Trento（特伦托大学数学系）；School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）
A Three-dimensional Edge-Based Interface Tracking (EBIT) Method for Multiphase-flow Simulations
Sorbonne Université（索邦大学）；CNRS, Institut Jean Le Rond d’Alembert UMR 7190（法国国家科学研究中心，让·勒朗·达朗贝尔研究所 UMR 7190）；State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University（西安交通大学航天学院，机械结构强度与振动国家重点实验室）；Università di Bologna（博洛尼亚大学）；Institut Universitaire de France（法兰西学术院）
