A hybrid lagrangian-eulerian approach for simulation of bubble dynamics

A mutiscale numerical approach is developed for the investigation of bubbly flows in turbulent environments. This consists of two different numerical approaches capable of capturing the bubble dynamics at different scales depending upon the relative size of the bubbles compared to the grid resolution: (i) fully resolved simulations (FRS) wherein the bubble dynamics and deformation are completely resolved, and (ii) subgrid, discrete bubble model where the bubbles are not resolved by the computational grid. For fully resolved simulations, a novel approach combining a particle-based, mesh-free technique with a finite-volume flow solver, is developed. The approach uses marker points around the interface and advects the signed distance to the interface in a Lagrangian frame. Interpolation kernel based derivative calculations typical of particle methods are used to extract the interface normal and curvature from unordered marker points. Unlike front-tracking methods, connectivity between the marker points is not necessary. For underresolved bubbles, a mixture-theory based Eulerian-Lagrangian approach accounting for volumetric displacements due to bubble motion and size variations is developed. The bubble dynamics is modeled by Rayleigh-Plesset equations using an adaptive timestepping scheme. A detailed verification and validation study of both approaches is performed to test the accuracy of the method on a variety of single and multiple bubble problems to show good predictive capability. Interaction of bubbles with a traveling vortex tube is simulated and compared with experimental data of Sridhar and Katz [1] to show good agreement.http://deepblue.lib.umich.edu/bitstream/2027.42/84270/1/CAV2009-final74.pd

Implicit smoothed particle hydrodynamics model for simulating incompressible fluid-elastic coupling

Fluid simulation has been one of the most critical topics in computer graphics for its capacity to produce visually realistic effects. The intricacy of fluid simulation manifests most with interacting dynamic elements. The coupling for such scenarios has always been challenging to manage due to the numerical instability arising from the coupling boundary between different elements. Therefore, we propose an implicit smoothed particle hydrodynamics fluid-elastic coupling approach to reduce the instability issue for fluid-fluid, fluid-elastic, and elastic-elastic coupling circumstances. By deriving the relationship between the universal pressure field with the incompressible attribute of the fluid, we apply the number density scheme to solve the pressure Poisson equation for both fluid and elastic material to avoid the density error for multi-material coupling and conserve the non-penetration condition for elastic objects interacting with fluid particles. Experiments show that our method can effectively handle the multiphase fluids simulation with elastic objects under various physical properties

Animating physical phenomena with embedded surface meshes

Accurate computational representations of highly deformable surfaces are indispensable in the fields of computer animation, medical simulation, computer vision, digital modeling, and computational physics. The focus of this dissertation is on the animation of physics-based phenomena with highly detailed deformable surfaces represented by triangle meshes. We first present results from an algorithm that generates continuum mechanics animations with intricate surface features. This method combines a finite element method with a tetrahedral mesh generator and a high resolution surface mesh, and it is orders of magnitude more efficient than previous approaches. Next, we present an efficient solution for the challenging problem of computing topological changes in detailed dynamic surface meshes. We then introduce a new physics-inspired surface tracking algorithm that is capable of preserving arbitrarily thin features and reproducing realistic fine-scale topological changes like Rayleigh-Plateau instabilities. This physics-inspired surface tracking technique also opens the door for a unique coupling between surficial finite element methods and volumetric finite difference methods, in order to simulate liquid surface tension phenomena more efficiently than any previous method. Due to its dramatic increase in computational resolution and efficiency, this method yielded the first computer simulations of a fully developed crown splash with droplet pinch off.Ph.D.Committee Chair: Turk, Greg; Committee Member: Essa, Irfan; Committee Member: Liu, Karen; Committee Member: Mucha, Peter J.; Committee Member: Rossignac, Jare

Surface-Only Simulation of Fluids

Surface-only simulation methods for fluid dynamics are those that perform computation only on a surface representation, without relying on any volumetric discretization. Such methods have superior asymptotic complexity in time and memory than the traditional volumetric discretization approaches, and thus are more tractable for simulation of complex fluid phenomena. Although for most computer graphics applications and many engineering applications, the interior flow inside the fluid phases is typically not of interest, the vast majority of existing numerical techniques still rely on discretization of the volumetric domain. My research first tackles the mesh-based surface tracking problem in the multimaterial setting, and then proposes surface-only simulation solutions for two scenarios: the soap-films and bubbles, and the general 3D liquids. Throughout these simulation approaches, all computation takes place on the surface, and volumetric discretization is entirely eliminated

Liquid simulation with mesh-based surface tracking

Animating detailed liquid surfaces has always been a challenge for computer graphics researchers and visual effects artists. Over the past few years, researchers in this field have focused on mesh-based surface tracking to synthesize extremely detailed liquid surfaces as efficiently as possible. This course provides a solid understanding of the steps required to create a fluid simulator with a mesh-based liquid surface. The course begins with an overview of several existing liquid-surface-tracking techniques and the pros and cons of each method. Then it explains how to embed a triangle mesh into a finite-difference-based fluid simulator and describes several methods for allowing the liquid surface to merge together or break apart. The final section showcases the benefits and further applications of a mesh-based liquid surface, highlighting state-of-the-art methods for tracking colors and textures, maintaining liquid volume, preserving small surface features, and simulating realistic surface-tension waves

Multimaterial Mesh-Based Surface Tracking

© ACM, 2014. 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 Da, F., Batty, C., & Grinspun, E. (2014). Multimaterial Mesh-Based Surface Tracking. Acm Transactions on Graphics, 33(4), 112. https://doi.org/10.1145/2601097.2601146We present a triangle mesh-based technique for tracking the evolution of three-dimensional multimaterial interfaces undergoing complex deformations. It is the first non-manifold triangle mesh tracking method to simultaneously maintain intersection-free meshes and support the proposed broad set of multimaterial remeshing and topological operations. We represent the interface as a non-manifold triangle mesh with material labels assigned to each half-face to distinguish volumetric regions. Starting from proposed application-dependent vertex velocities, we deform the mesh, seeking a non-intersecting, watertight solution. This goal necessitates development of various collision-safe, label-aware non-manifold mesh operations: multimaterial mesh improvement; T1 and T2 processes, topological transitions arising in foam dynamics and multiphase flows; and multimaterial merging, in which a new interface is created between colliding materials. We demonstrate the robustness and effectiveness of our approach on a range of scenarios including geometric flows and multiphase fluid animation.This work was supported in part by the NSF (Grants IIS-1319483, CMMI-1331499, IIS-1217904, IIS-1117257, CMMI-1129917, IIS-0916129), the Israel-US Binational Science Founda-tion, the Natural Sciences and Engineering Research Council of Canada (NSERC), Intel, The Walt Disney Company, Autodesk, Side Effects Software, NVIDIA, and the Banting Postdoctoral Fel-lowships program

A practical octree liquid simulator with adaptive surface resolution

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2020 Copyright held by the owner/author(s). Publication rights licensed to ACM. 0730-0301/2020/7-ART32 $15.00 https://doi.org/10.1145/3386569.3392460We propose a new adaptive liquid simulation framework that achieves highly detailed behavior with reduced implementation complexity. Prior work has shown that spatially adaptive grids are efficient for simulating large-scale liquid scenarios, but in order to enable adaptivity along the liquid surface these methods require either expensive boundary-conforming (re-)meshing or elaborate treatments for second order accurate interface conditions. This complexity greatly increases the difficulty of implementation and maintainability, potentially making it infeasible for practitioners. We therefore present new algorithms for adaptive simulation that are comparatively easy to implement yet efficiently yield high quality results. First, we develop a novel staggered octree Poisson discretization for free surfaces that is second order in pressure and gives smooth surface motions even across octree T-junctions, without a power/Voronoi diagram construction. We augment this discretization with an adaptivity-compatible surface tension force that likewise supports T-junctions. Second, we propose a moving least squares strategy for level set and velocity interpolation that requires minimal knowledge of the local tree structure while blending near-seamlessly with standard trilinear interpolation in uniform regions. Finally, to maximally exploit the flexibility of our new surface-adaptive solver, we propose several novel extensions to sizing function design that enhance its effectiveness and flexibility. We perform a range of rigorous numerical experiments to evaluate the reliability and limitations of our method, as well as demonstrating it on several complex high-resolution liquid animation scenarios.This research was supported by the JSPS Grant-in-Aid for Young Scientists (18K18060) and the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-04360-2014)

고차 정확도 라그랑지안 표면 추적 문제에 대한 연구

학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 2. 강명주.In this thesis, we proposed the method for tracking the interface with higher order accuracy, when given the normal velocity. Our proposed model combines the well-known Lagrangian surface tracking method with the high order interpolation method for discontinuity capturing. The proposed method not only tracks the surface with higher accuracy than the conventional method, but also depends little on the geometric parameters. Furthermore, the method accurately detects the local shapes of the surface, which is an essential part for a stable interface tracking method. The model developed on the two-dimensional interface can be extended naturally on the three-dimensional interface using the high order interpolation method on triangular meshes.1 Introduction 1 2 Previous works 4 2.1 Level set method 4 2.1.1 Basic equations 4 2.1.2 Numerical discretization 5 2.1.3 Reinitialization 6 2.2 Face offsetting method 8 2.2.1 Advection type 8 2.2.2 Wavefrontal type 11 2.2.3 Null-space smoothing 13 2.3 Weighted essentially non-oscillatory scheme 14 2.3.1 Polynomial reconstruction 14 2.3.2 ENO reconstruction 15 2.3.3 WENO reconstruction 16 2.4 WENO scheme on triangular meshes 20 2.4.1 Third order reconstruction 20 2.4.2 Fourth order reconstruction 22 2.4.3 Positivity of linear weights 23 2.4.4 Smoothness indicators and nonlinear weights 25 2.5 Total variation diminishing Runge-Kutta method 26 3 Proposed models 28 3.1 FOM-WENO scheme 28 3.1.1 Motivations for high order FOM scheme 28 3.1.2 High order reconstruction of normals 30 3.1.3 Modified normal vector and error analysis 32 3.1.4 Setting functions reflecting geometric shocks 35 3.1.5 Mesh smoothing method 37 3.1.6 FOM-WENO algorithm 37 3.2 FOM-WENO scheme in three dimension 39 3.3 Numerical experiments 42 3.3.1 Accuracy for normal vector approximation 43 3.3.2 Long time accuracy for corner propagation 51 3.3.3 Geometric stability of FOM-WENO scheme 60 3.3.4 Comparison of volume loss 62 3.3.5 Propagating under non-uniform normal velocity 66 3.3.6 Results in three dimension 68 4 Conclusion 73 Abstract (in Korean) 80Docto

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Fast fully automatic myocardial segmentation in 4D cine cardiac magnetic resonance datasets

Dissertação de mestrado integrado em Engenharia BiomédicaCardiovascular diseases (CVDs) are the leading cause of death in the world, representing 30% of all global deaths. Among others, assessment of the left ventricular (LV) morphology and global function using non-invasive cardiac imaging is an interesting technique for diagnosis and treatment follow-up of patients with CVDs. Nowadays, cardiac magnetic resonance (CMR) imaging is the gold-standard technique for the quantification of LV volumes, mass and ejection fraction, requiring the delineation of endocardial and epicardial contours of the left ventricle from cine MR images. In clinical practice, the physicians perform this segmentation manually, being a tedious, time consuming and unpractical task. Even though several (semi-)automated methods have been presented for LV CMR segmentation, fast, automatic and optimal boundaries assessment is still lacking, usually requiring the physician to manually correct the contours. In the present work, we propose a novel fast fully automatic 3D+time LV segmentation framework for CMR datasets. The proposed framework presents three conceptual blocks: 1) an automatic 2D mid-ventricular initialization and segmentation; 2) an automatic stack initialization followed by a 3D segmentation at the end-diastolic phase; and 3) a tracking procedure to delineate both endo and epicardial contours throughout the cardiac cycle. In each block, specific CMR-targeted algorithms are proposed for the different steps required. Hereto, we propose automatic and feasible initialization procedures. Moreover, we adapt the recent B-spline Explicit Active Surfaces (BEAS) framework to the properties of CMR image segmentation by integrating dedicated energy terms and making use of a cylindrical coordinate system that better fits the topology of CMR data. At last, two tracking methods are presented and compared. The proposed framework has been validated on 45 4D CMR datasets from a publicly available database and on a large database from an ongoing multi-center clinical trial with 318 4D datasets. In the technical validation, the framework showed competitive results against the state-of-the-art methods, presenting leading results in both accuracy and average computational time in the common database used for comparative purposes. Moreover, the results in the large scale clinical validation confirmed the high feasibility and robustness of the proposed framework for accurate LV morphology and global function assessment. In combination with the low computational burden of the method, the present methodology seems promising to be used in daily clinical practice.As doenças cardiovasculares (DCVs) são a principal causa de morte no mundo, representando 30% destas a nível global. Na prática clínica, uma técnica empregue no diagnóstico de pacientes com DCVs é a avaliação da morfologia e da função global do ventrículo esquerdo (VE), através de técnicas de imagiologia não-invasivas. Atualmente, a ressonância magnética cardíaca (RMC) é a modalidade de referência na quantificação dos volumes, massa e fração de ejeção do VE, exigindo a delimitação dos contornos do endocárdio e epicárdio a partir de imagens dinâmicas de RMC. Na prática clínica diária, o método preferencial é a segmentação manual. No entanto, esta é uma tarefa demorada, sujeita a erro humano e pouco prática. Apesar de até à data diversos métodos (semi)-automáticos terem sido apresentados para a segmentação do VE em imagens de RMC, ainda não existe um método capaz de avaliar idealmente os contornos de uma forma automática, rápida e precisa, levando a que geralmente o médico necessite de corrigir manualmente os contornos. No presente trabalho é proposta uma nova framework para a segmentação automática do VE em imagens 3D+tempo de RMC. O algoritmo apresenta três blocos principais: 1) uma inicialização e segmentação automática 2D num corte medial do ventrículo; 2) uma inicialização e segmentação tridimensional no volume correspondente ao final da diástole; e 3) um algoritmo de tracking para obter os contornos ao longo de todo o ciclo cardíaco. Neste sentido, são propostos procedimentos de inicialização automática com elevada robustez. Mais ainda, é proposta uma adaptação da recente framework “B-spline Explicit Active Surfaces” (BEAS) com a integração de uma energia específica para as imagens de RMC e utilizando uma formulação cilíndrica para tirar partido da topologia destas imagens. Por último, são apresentados e comparados dois algoritmos de tracking para a obtenção dos contornos ao longo do tempo. A framework proposta foi validada em 45 datasets de RMC provenientes de uma base de dados disponível ao público, bem como numa extensa base de dados com 318 datasets para uma validação clínica. Na avaliação técnica, a framework proposta obteve resultados competitivos quando comparada com outros métodos do estado da arte, tendo alcançado resultados de precisão e tempo computacional superiores a estes. Na validação clínica em larga escala, a framework provou apresentar elevada viabilidade e robustez na avaliação da morfologia e função global do VE. Em combinação com o baixo custo computacional do algoritmo, a presente metodologia apresenta uma perspetiva promissora para a sua aplicação na prática clínica diária