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We have established a parallel, adaptive interface-tracking framework in order to conduct, based on the framework, direct simulation of binary head-on droplet collision in the high-Weber-number regime (from 200 to 1500) that exhibits complex topological changes and substantial length scale variations. The overall algorithms include a combined Eulerian and Lagrangian solver to track moving interfaces, conservative Lagrangian mesh modification and reconstruction, cell-based unstructured adaptive mesh refinement (AMR) in the Eulerian solver, and associated Eulerian and Lagrangian domain partitions to minimize communication overhead. Based on the combined computational and experimental efforts, we have resolved for the first time the free-surface instabilities of the colliding droplets at such high Weber number. We detail the characteristics of coalescence, stretch, end pinching, fingering, free-surface movement and drop breakup. The Taylor–Culick rim is present soon after the collision. Furthermore, we observe two types of longitudinal instabilities on the rim, namely, the Rayleigh–Taylor (RT)-type instability in the initial deceleration phase of the circular sheet right after droplet coalescence, and later the Rayleigh–Plateau (RP) instabilities. As the Taylor–Culick rim disintegrates in the retraction phase, fingering effect is profound and resulting in wider droplet size distribution.

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In this study, we present a parallelized adaptive moving boundary computation technique on distributed memory multi-processor systems for multi-scale multiphase flow simulations. The solver utilizes the Eulerian-Lagrangian method to track moving (Lagrangian) interfaces explicitly on the stationary (Eulerian) Cartesian grid where the flow fields are computed. Since there exists strong data and task dependency between two distinct Eulerian and Lagrangian domain, we address the decomposition strategies for each domain separately. We then propose a trade-off approach aiming for parallel scalability. Spatial domain decomposition is adopted for both Eulerian and Lagrangian domains for load balancing and data locality to minimize inter-processor communication. In addition, a cellbased unstructured parallel adaptive mesh refinement (AMR) technique is implemented for the flexible local refinement with efficient grid usage and even-distributed computational workload among processors. The parallel performance is evaluated independently for the Cartesian grid solver and sub-procedures in cell-based unstructured AMR. The capability and the overall performance of the parallel adaptive Eulerian-Lagrangian method including moving boundary and topological change is demonstrated by modeling binary droplet collisions. With the aid of the present techniques, large scale moving boundary problems can be effectively computed.

A multi-scale multiphase computational model including phase change has been developed to study the moving interfacial dynamics and thermal effect in various engineering and scientific applications, including spacecraft cryogenic propellant delivery processes. A 3-D adaptive Eulerian-Lagrangian method is implemented, utilizing the stationary (Eulerian) frame to resolve the flow field, and the marker-based triangulated moving (Lagrangian) surface meshes to treat the fluid interface and solid boundaries. Other than treating the unsteady, convection, pressure, viscous/diffusion, and buoyancy terms in the governing field equations, the energy and mass transfer across interface due to phase change is handled using probe-based profile computations. Numerous test cases are presented, including liquid fuel draining, sloshing, and surface flow stability related to the interfacial dynamics, and natural convection in a cavity and Stefan problem for energy transport and phase change dynamics.