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The unsteady motion of a gas-liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here we explore the use of skeletonization to identify the minimum amount of information needed to describe their geometry. We skeletonize a periodic liquid jet by a modification of a recently introduced approach to coarsen multiphase flows while retaining a sharp interface. The process consists of diffusing an index function and at the same time moving the interfaces with it, until they "collapse" into each other and form skeletons. The skeleton represents the basic topology of the jet and we also keep track of how much the interface is moved (or how much volume is "accumulated") during the process, which can be used to approximately reconstruct the jet. We explore various quantitative measures to characterize and distinguish the skeletons. Those include standard morphometrics such as branch length distribution, after segmenting the skeletons into branches, and a more sophisticated representation of the skeleton structures called Topology Morphology Descriptor (TMD), to obtain an "equivalent" description of the skeletons by retaining information about the topology in a compact way.

Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of time and energy. In this paper, we propose communication-efficient parallel algorithms for solving partial differential equations that alleviate this overhead. First, we describe an asynchronous algorithm that removes the requirement of synchronization and checks for termination in a distributed fashion while maintaining the provision to restart iterations if necessary. Then, we build on the asynchronous algorithm to propose an event-triggered communication algorithm that communicates the boundary values to neighboring processors only at certain iterations, thereby reducing the number of messages while maintaining similar accuracy of solution. We demonstrate our algorithms on a successive over-relaxation solver for the Pressure Poisson equation arising from variable density incompressible multiphase flows in 3-D and show that our algorithms improve time and energy efficiency., Comment: Under Review

Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be important to retain a sharp interface for the resolved scales. Here, a process to coarsen or filter fully resolved numerical solutions for incompressible multiphase flows while retaining a sharp interface is examined. The different phases are identified by an index function that takes different values in each phase and is coarsened by solving a constant coefficient diffusion equation, while tracking the interface contour. Small flows scales of one phase, left behind when the interface is moved, are embedded in the other phase by solving another diffusion equation with a modified diffusion coefficient that is zero at the interface location to prevent diffusion across the interface, plus a pressure like equation to enforce incompressibility of the coarse velocity field. Examples of different levels of coarsening are shown. A simulation of a coarse model, where small scales are treated as a homogeneous mixture, results in a solution that is similar to the filtered fully resolved field for the early time Rayleigh-Taylor instability.

Machine learning is used to develop closure terms for coarse grained model of two-dimensional turbulent flow directly from the coarse grained data by adding a source term to the Navier-Stokes equations to ensure that the coarse-grained flow evolves in the correct way. The source term is related to the average flow using a Neural Network with a relatively simple structure and smoothed slightly to prevent instabilities in a posteriori test. The time dependent coarse grained flow field is generated by filtering fully resolved results and the predicted coarse field evolution agrees well with the filtered results, both for the flow used to learn the closure terms and for flows not used for the learning.

In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface separating two immiscible fluids, given the volume fraction in the cell and the adjacent cells. Currently, the most accurate approach is to fit a curve (2D), or a surface (3D), matching the volume fractions and finding the curvature by differentiation. Here, a different approach is examined. A synthetic data set, relating curvature to volume fractions, is generated using well-defined shapes where the curvature and volume fractions are easily found and then machine learning is used to fit the data (training). The resulting function is used to find the curvature for shapes not used for the training and implemented into a code to track moving interfaces. The results suggest that using machine learning to generate the relationship is a viable approach that results in reasonably accurate predictions.

Purpose - This paper continues the development of a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach - A front-tracking/finite volume method introduced in Part I to simulate the heat transfer and fluid dynamics of the deposition of a polymer filament on a fixed bed is extended by adding an improved model for the injection nozzle, including the shrinkage of the polymer as it cools down, and accounting for stresses in the solid. Findings - The accuracy and convergence properties of the new method are tested by grid refinement and the method is shown to produce convergent solutions for the shape of the filament, the temperature distribution, the shrinkage and the solid stresses. Research limitations/implications - The method presented in the paper focuses on modeling the fluid flow, the cooling and solidification, as well as volume changes and residual stresses, using a relatively simple viscoelastic constitutive model. More complex material models, depending, for example, on the evolution of the configuration tensor, are not included. Practical implications - The ability to carry out fully resolved numerical simulations of the fusion deposition process is expected to be critical for the validation of mathematical models for the material behavior, to help explore new deposition strategies, and to provide the "ground truth" for the development of reduced order models. Originality/value - The paper completes the development of the first numerical method for fully resolved simulation of fusion filament modeling., Comment: Accepted by Rapid Prototyping Journal

Purpose - This paper presents a first step toward developing a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach - A front-tracking/finite volume method previously developed for simulations of multiphase flows is extended to model the injection of hot polymer and its cooling down. Findings - The accuracy and convergence properties of the new method are tested by grid refinement and the method is shown to produce convergent solutions for the shape of the filament, the temperature distribution, contact area and reheat region when new filaments are deposited on top of previously laid down filaments. Research limitations/implications - The present paper focuses on modeling the fluid flow and the cooling. The modeling of solidification, volume changes and residual stresses will be described in Part II. Practical implications - The ability to carry our fully resolved numerical simulations of the fusion deposition process is expected to help explore new deposition strategies and to provide the "ground truth" for the development of reduced order models. Originality/value - The present paper is the first fully resolved simulation of the deposition in fusion filament modeling., Comment: Accepted by Rapid Prototyping Journal

Spray formation and atomization in a gas-liquid mixing layer is an important fundamental problem of multiphase flows. It is highly desirable to visualize the detailed atomization process and to analyze the instabilities and mechanisms involved, and massive numerical simulations are required, in addition to experiment. Rapid development of numerical methods and computer technology in the past decades now allows large-scale three-dimensional direct numerical simulations of atomization to be performed. Nevertheless, the fundamental question, whether all the physical scales involved in the primary breakup process are faithfully resolved, remains unclear. In the present study, we conduct direct numerical simulations of spray formation in a gas-liquid mixing layer with state-of-the-art computational resources (using up to 4 billion cells and 16384 cores), in order to obtain a high-fidelity numerical closeup of the detailed mechanisms of spray formation. We also aim to examine whether present computational resources are sufficient for a fully resolved direct numerical simulation of atomization.

In the computation of multiphase flow with mass transfer, the large disparity between the length and time scale of the mass transfer and the fluid flow demand excessive grid resolution for fully resolved simulation of such flow. We have developed a subscale description for the mass transfer in bubbly flow to alleviate the grid requirement needed at the interface where the mass gets transferred from one side to the other. In this fluid dynamics video, a simulation of the mass transfer from buoyant bubbles is done using a Front Tracking method for the tracking of interface and a subscale description for the transfer of mass from the bubble into the domain. After the mass is transferred from the bubble into the domain, mass is followed by solving an advection-diffusion equation on a relatively coarse Cartesian grid. More detail about the method can be found in our paper. This simulation shows 13 moving bubbles in a periodic domain, 3db X 3db X 48db, where db is the bubble diameter. The grid resolution is 64 X 64 X 1024, which results in about 21 cell across one bubble diameter. The flow non-dimensional governing parameters are Eo = 2.81 and Mo = 4.5 * 10^-7 with density and viscosity ratio of 0.1 and for the mass transfer we have Sc = 60. In the movie, bubbles are colored to show the mass boundary layer thickness, with blue showing a close to zero value and red showing the maximum value. Mass concentration inside the domain is colored from transparent blue for low value, 0, to solid red for high value, 1. Time is non-dimensionalized with sqrt(db/g)., Comment: No figure, 2 video, one low and one high resolution version, added acknowledgements to the videos and reduced the high resolution file size

This article describes the fluid dynamics video: "Effect of bubble deformability on the vertical channel bubbly flow". The effect of bubble deformability on the flow rate of bubbly upflow in a turbulent vertical channel is examined using direct numerical simulations. A series of simulations with bubbles of decreasing deformability reveals a sharp transition from a flow with deformable bubbles uniformly distributed in the middle of the channel to a flow with nearly spherical bubbles with a wall-peak bubble distribution and a much lower flow rate., Comment: Two videos are included

This article describes the fluid dynamics video: "Turbulent Bubbly Channel Flow: Role of Bubble Deformability." The effect of bubble deformability on the flow rate of bubbly upflow in a turbulent vertical channel is examined using direct numerical simulations. A series of simulations with bubbles of decreasing deformability shows a transition from flow where deformable bubbles remain in the middle of the channel to a situation where nearly spherical bubbles slide along the walls.