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Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

A key part of emerging advanced additive manufacturing methods is the deposition of specialized particulate mixtures of materials on substrates. For example, in many cases these materials are polydisperse powder mixtures whereby one set of particles is chosen with the objective to electrically, thermally or mechanically functionalize the overall mixture material and another set of finer-scale particles serves as an interstitial filler/binder. Often, achieving controllable, precise, deposition is difficult or impossible using mechanical means alone. It is for this reason that electromagnetically-driven methods are being pursued in industry, whereby the particles are ionized and an electromagnetic field is used to guide them into place. The goal of this work is to develop a model and simulation framework to investigate the behavior of a deposition as a function of an applied electric field. The approach develops a modular discrete-element type method for the simulation of the particle dynamics, which provides researchers with a framework to construct computational tools for this growing industry.

A Lagrangian scheme that combines Voronoi diagrams with smoothed particle hydrodynamics (SPH) for incompressible flows has been developed. Within the Voronoi tessellation, the Voronoi particle hydrodynamics (VPH) method is used, which is structurally similar to SPH. Two sub-domains are defined based on the proximity to the boundaries. The VPH formulation is used for particles close to solid boundaries, where SPH consistency and implementation of boundary conditions become problematic. Some overlapping of both sub-domains is allowed in order to provide a buffer zone to progressively transition from one method to the other. An explicit weakly compressible formulation for both sub-domains is used, with the diffusive term from the δ-SPH correction extended to the VPH formulation. In addition, the density field is periodically re-initialized and a shifting algorithm is included to avoid excessive deformation of the Voronoi cells. Solid, free-surface, and inlet/outlet boundary conditions are considered. A linear damping term is used during the initialization process to mitigate possible inconsistencies from the user-defined initial conditions. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

This work presents a computer simulation framework based on discrete element method to analyze manufacturing processes that comprise a loosely flowing stream of particles in a carrier fluid being deposited on a target surface. The individual particulate dynamics under the combined action of particle collisions, fluid-particle interactions, particle-surface contact and adhesive interactions is simulated, and aggregated to obtain global system behavior. A model for deposition which incorporates the effect of surface energy, impact velocity and particle size, is developed. The fluid-particle interaction is modeled using appropriate spray nozzle gas velocity distributions and a one-way coupling between the phases. It is found that the particle response times and the release velocity distribution of particles have a combined effect on inter-particle collisions during the flow along the spray. It is also found that resolution of the particulate collisions close to the target surface plays an important role in characterizing the trends in the deposit pattern. Analysis of the deposit pattern using metrics defined from the particle distribution on the target surface is provided to characterize the deposition efficiency, deposit size, and scatter due to collisions.

This work addresses the impact and deposition of charged ''cluster-droplets'', comprised of particulates, on electrified surfaces. A direct numerical method is developed, based on an implicit, staggered, time-stepping scheme which separates the impulsive and continuous forces between particles, in conjunction with an iterative solution method that automatically adapts the time-step sizes to control the rates of convergence within a time-step. This approach is used to investigate the post-impact structure of charged particulate cluster-droplets. Particulate cluster-droplet impact has wide-ranging application to areas such as inkjet printing, sprays, coatings, etc. A series of numerical examples are provided, where we investigate the effect of progressively increasing the electric field strength on the impacted substrate, leading to a more coherent cluster deposition. An analysis is also provided for the interaction of charged cluster-droplets with electromagnetic fields.