Parallel simulation of incompressible free-surface flows

A large number of computational problems and physical phenomena in areas such as fluid mechanics involve the motion of interfaces. Simulation of this type of problems is challenging. In this dissertation, an Arbitrary Lagrangian Eulerian (ALE) formulation is rigorously derived and a reduced form of ALE is implemented with various surface tracking techniques to simulate capillary jet breakup on a superposition-based parallel platform. The ALE formulation starts with an integral approach on moving control volumes and is converted into a format consistent with method-of-lines discretization. The weighted ALE is also formulated. Contradictions in existing differential approach of ALE formulation are pointed out and the paradoxical issue is clarified. The reduced ALE is used for formulation of incompressible Navier-Stokes flows on moving meshes. An indirect boundary tracking of flux method, decoupled non-Lagrangian direct boundary tracking (DBT), iterative non-Lagrangian DBT, and Lagrangian DBT are implemented for the highly sensitive capillary jet breakup. Excellent numerical results are obtained, which vindicates the success of the overall numerical method. The simulation is based on a superposition-based non-numeric parallelization, which takes a different approach from conventional domain decomposition. Element-by-element construction, superposition-based partition, and condensed random data structure are used for the data structure aspect of the parallelization. From the algorithm aspect of the parallelization, it maintains the same flow of data, control of process, and global structure as the serial counterpart. As a result, the parallelization features simplicity and portability in implementation yet achieves moderate performance. A three-dimensional semi-discontinuous finite element method serves as the domain solver for all calculations, and is adequately verified with fixed-geometry benchmark problems. Various time schemes, including a proposed linear implicit scheme with excellent performance, are implemented generically. The indefinite system as a result of incompressible flows is tackled with a proposed discrete operator splitting technique, which breaks a large ill-natured discrete equation system into well-natured subsystems through source-term iterations.