An implicit surface tension model for the analysis of droplet dynamics

A Lagrangian incompressible fluid flow model is extended by including an implicit surface tension term in order to analyze droplet dynamics. The Lagrangian framework is adopted to model the fluid and track its boundary, and the implicit surface tension term is used to introduce the appropriate forces at the domain boundary. The introduction of the tangent matrix corresponding to the surface tension force term ensures enhanced stability of the derived model. Static, dynamic and sessile droplet examples are simulated to validate the model and evaluate its performance. Numerical results are capable of reproducing the pressure distribution in droplets, and the advancing and receding contact angles evolution for droplets in varying substrates and inclined planes. The model is stable even at time steps up to 20 times larger than previously reported in literature and achieves first and second order convergence in time and space, respectively. The present implicit surface tension implementation is applicable to any model where the interface is represented by a moving boundary mesh.Peer ReviewedPostprint (published version

Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps

© ACM, 2016. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Azevedo, V. C., Batty, C., & Oliveira, M. M. (2016). Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps. Acm Transactions on Graphics, 35(4), 97. https://doi.org/10.1145/2897824.292591Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.Conselho Nacional de Desenvolvimento Científico e Tecnológico, Natural Sciences and Engineering Research Council of Canad

The Mimetic Approach to Incompressible Surface Tension Flows

Water has many aesthetic properties that can have a strong impact on our perceptions. For instance, coffee can bring a feeling of liveliness, rain drops on a window may spark nostalgia, morning dew on a leaf can suggest freshness, and melting icicles remind us of spring. The ubiquity of water and the complexity of phenomena it can exhibit makes it an important and interesting topic for simulation in computer graphics, where the focus lies in visual aesthetics. Our focus is to produce a method for simulating water droplets at scales where surface tension effects are visually significant. These are precisely the scales in the scenarios mentioned above. We propose a simple new approach to simulating water-like liquids with visible surface tension effects in two dimensions. We employ a recently developed Mimetic Finite Difference (MFD) method to solve the Poisson problem, which enforces incompressibility in the incompressible Euler equations. Using a cut-cell discretization, the MFD method allows us to extend the ubiquitous finite difference method on a Marker-and- Cell (MAC) discretization to handle irregular boundaries. To produce surface tension effects, we keep track of an explicit Lagrangian surface that conforms exactly to the simulation mesh. To achieve stable results, we adapt a semi-implicit surface tension scheme [Misztal et al., 2012] to our MFD pressure solve, which allows us to use time steps about 2-3 times larger than the corresponding explicit method. In addition, the semi-implicit method is extended to simulate liquids in contact with hydrophobic and hydrophilic surfaces. To provide stable surface tracking, we employ a method based on marching square templates [Rocchini et al., 2001; Müller, 2009] augmented by two simple techniques for improving mesh quality. Collapsing small interior grid edges near the fluid surface eliminates triangle elements with small angles near the liquid surface. Eliminating cells with small angles gives a better bound on the conditioning of the discrete Laplacian used in the Poisson solve, hence adding stability to our simulation. To compute surface tension forces, we use a version of the surface mesh that has been perturbed to reduce the number of short edges, in order to more robustly estimate surface curvature. These are essential for stability when coupling the MFD solve with surface tension forces. Our approach employs a unique combination of methods to address the problem of accurately tracking the contact between liquid and solid surfaces. We propose a method that couples well with the majority of fluid simulators used in the visual effects industry, while introducing a stable surface tension technique that doesn’t require complex auxiliary meshing strategies [Zheng et al., 2015]

Methods for the Modeling and Simulation of Sprays and Other Interfacial Flows

University of Minnesota Ph.D. dissertation. September 2019. Major: Mechanical Engineering. Advisor: Sean Garrick. 1 computer file (PDF); xix, 172 pages.Interfacial multiphase flows involve the motion of at least two fluids separated by surface tension. Atomizing interfacial flows, colloquially known as sprays, are among the most important fluid dynamic systems because of their ubiquity; power generation, delivery of aerosolized medicines, and productive produce farming all depend fundamentally on the detailed control of sprays. Atomization remains poorly understood because of a historical and persisting inability to accurately and affordably measure the dynamics inside and near the spray orifice outlet -- it is therefore desirable to be able to numerically simulate sprays with high fidelity. This dissertation presents computational methods that aim to improve current shortcomings in the modeling and simulation of sprays. Accurately characterizing the interfacial curvature of poorly-resolved liquid structures is addressed by deriving a series of finite particle methods for computing curvature. The methods are verified in analytical curvature tests, and validated against the oscillation frequency of ethanol droplets in air. The finite particle method, leveraging dynamic length scale modification, is demonstrated to out-perform the widely-used height function approach. Tracking the location of interfaces is also addressed, for which a coupled Eulerian-Lagrangian point mass particle scheme is introduced that preserves a well-distributed particle field, can be applied to an arbitrary number of fluids, and does not limit the simulation time step. The Eulerian-Lagrangian method is demonstrated to out-perform contemporary geometric volume of fluid methods at resolutions relevant to spray simulation in a variety of analytical phase tracking tests, and is dynamically evaluated by simulating extending three-phase elliptical regions, droplet dynamics, and Rayleigh-Taylor instabilities. The Eulerian-Lagrangian method is then extended to an approach for consistently and conservatively solving multiphase convection-diffusion problems -- this extension is verified via two analytical heat transfer problems, and robustness is demonstrated by simulating heated air blast atomization. Each of these tests conserves thermal energy and preserves boundedness of the temperature field. This dissertation concludes by outlining paths for consistently and conservatively solving the multiphase Navier-Stokes equations and the multiphase large eddy simulation equations in the coupled Eulerian-Lagrangian point mass particle framework