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

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

Interface Tracking and Solid-Fluid Coupling Techniques with Coastal Engineering Applications

Multi-material physics arise in an innumerable amount of engineering problems. A broadly scoped numerical model is developed and described in this thesis to simulate the dynamic interaction of multi-fluid and solid systems. It is particularly aimed at modelling the interaction of two immiscible fluids with solid structures in a coastal engineering context; however it can be extended to other similar areas of research. The Navier Stokes equations governing the fluids are solved using a combination of finite element (FEM) and control volume finite element (CVFE) discretisations. The sharp interface between the fluids is obtained through the compressive transport of material properties (e.g. material concentration). This behaviour is achieved through the CVFE method and a conveniently limited flux calculation scheme based on the Hyper-C method by Leonard (1991). Analytical and validation test cases are provided, consisting of steady and unsteady flows. To further enhance the method, improve accuracy, and exploit Lagrangian benefits, a novel moving mesh method is also introduced and tested. It is essentially an Arbitrary Lagrangian Eulerian method in which the grid velocity is defined by semi-explicitly solving an iterative functional minimisation problem. A multi-phase approach is used to introduce solid structure modelling. In this approach, solution of the velocity field for the fluid phase is obtained using Model B as explained by Gidaspow (1994, page 151). Interaction between the fluid phase and the solids is achieved through the means of a source term included in the fluid momentum equations. The interacting force is calculated through integration of this source term and adding a buoyancy contribution. The resulting force is passed to an external solid-dynamics model such as the Discrete Element Method (DEM), or the combined Finite Discrete Element Method (FEMDEM). The versatility and novelty of this combined modelling approach stems from its ability to capture the fluid interaction with particles of random size and shape. Each of the three main components of this thesis: the advection scheme, the moving mesh method, and the solid interaction are individually validated, and examples of randomly shaped and sized particles are shown. To conclude the work, the methods are combined together in the context of coastal engineering applications, where the complex coupled problem of waves impacting on breakwater amour units is chosen to demonstrate the simulation possibilities. The three components developed in this thesis significantly extend the application range of already powerful tools, such as Fluidity, for fluids-modelling and finite discrete element solids-modelling tools by bringing them together for the first time

A Lagrangian-Eulerian simulation method for viscoelastic flows applied to adhesive joining

Viscoelastic flows are important for many industrial processes, such as adhesive joining, polymer extrusion and additive manufacturing. Numerical simulations enable virtual evaluation and product realization, which can support the design phase and reduce the amount of costly physical testing. However, such applications are challenging to simulate. Thus, efficient, robust and user-friendly simulation methods are needed. In this thesis, a Lagrangian--Eulerian simulation framework for viscoelastic flow is presented. The constitutive equation is solved at Lagrangian nodes, convected by the flow, while the momentum and continuity equations are discretized with the finite volume method. The volume of fluid method is used to model free-surface flow, with an injection model for extrusion along arbitrary nozzle paths. The solver combines an automatic and adaptive octree background grid with implicit immersed boundary conditions. In contrast to boundary-conformed mesh techniques, the framework handles arbitrary geometry and moving objects efficiently. Furthermore, novel coupling methods between the Lagrangian and Eulerian solutions as well as unique treatment of the Lagrangian stresses at the fluid-fluid interface are developed. Consequently, the resulting method can simulate the complex flows associated with the intended applications, without the need for advanced stabilization techniques. The framework is validated for a variety of flows, including relevant benchmarks as well as industrial adhesive joining applications. The latter includes robot-carried adhesive extrusion onto a car fender as well as a hemming application. The results agree with the available experimental data. As such, the research presented in this thesis can contribute to enable virtual process development for joining applications

Adaptive mesh refinement method for CFD applications

The main objective of this thesis is the development of an adaptive mesh refinement (AMR) algorithm for computational fluid dynamics simulations using hexahedral and tetrahedral meshes. This numerical methodology is applied in the context of large-eddy simulations (LES) of turbulent flows and direct numerical simulations (DNS) of interfacial flows, to bring new numerical research and physical insight. For the fluid dynamics simulations, the governing equations, the spatial discretization on unstructured grids and the numerical schemes for solving Navier-Stokes equations are presented. The equations follow a discretization by conservative finite-volume on collocated meshes. For the turbulent flows formulation, the spatial discretization preserves symmetry properties of the continuous differential operators and the time integration follows a self-adaptive strategy, which has been well tested on unstructured grids. Moreover, LES model consisting of a wall adapting local-eddy-viscosity within a variational multi-scale formulation is used for the applications showed in this thesis. For the two-phase flow formulation, a conservative level-set method is applied for capturing the interface between two fluids and is implemented with a variable density projection scheme to simulate incompressible two-phase flows on unstructured meshes. The AMR algorithm developed in this thesis is based on a quad/octree data structure and keeps a relation of 1:2 between levels of refinement. In the case of tetrahedral meshes, a geometrical criterion is followed to keep the quality metric of the mesh on a reasonable basis. The parallelization strategy consists mainly in the creation of mesh elements in each sub-domain and establishes a unique global identification number, to avoid duplicate elements. Load balance is assured at each AMR iteration to keep the parallel performance of the CFD code. Moreover, a mesh multiplication algorithm (MM) is reported to create large meshes, with different kind of mesh elements, but preserving the topology from a coarser original mesh. This thesis focuses on the study of turbulent flows and two-phase flows using an AMR framework. The cases studied for LES of turbulent flows applications are the flow around one and two separated square cylinders, and the flow around a simplified car model. In this context, a physics-based refinement criterion is developed, consisting of the residual velocity calculated from a multi-scale decomposition of the instantaneous velocity. This criteria ensures grid adaptation following the main vortical structures and giving enough mesh resolution on the zones of interest, i.e., flow separation, turbulent wakes, and vortex shedding. The cases studied for the two-phase flows are the DNS of 2D and 3D gravity-driven bubble, with a particular focus on the wobbling regime. A study of rising bubbles in the wobbling regime and the effect of dimensionless numbers on the dynamic behavior of the bubbles are presented. Moreover, the use of tetrahedral AMR is applied for the numerical simulation of gravity-driven bubbles in complex domains. On this topic, the methodology is validated on bubbles rising in cylindrical channels with different topology, where the study of these cases contributed to having new numerical research and physical insight in the development of a rising bubble with wall effects.El objetivo principal de esta tesis es el desarrollo de un algoritmo adaptativo de refinamiento de malla (AMR) para simulaciones de dinámica de fluidos computacional utilizando mallas hexaédricas y tetraédricas. Esta metodología numérica se aplica en el contexto de simulaciones Large-eddie (LES) de flujos turbulentos y simulaciones numéricas directas (DNS) de flujos interfaciales, para traer nuevas investigaciones numéricas y entendimiento físicas. Para las simulaciones de dinámica de fluidos, se presentan las ecuaciones governantes, la discretización espacial en mallas no estructuradas y los esquemas numéricos para resolver las ecuaciones de Navier-Stokes. Las ecuaciones siguen una discretización conservativa por volumenes finitos en mallas colocadas. Para la formulación de flujos turbulentos, la discretización espacial preserva las propiedades de simetría de los operadores diferenciales continuos y la integración de tiempo sigue una estrategia autoadaptativa, que ha sido bien probada en mallas no estructuradas. Además, para las aplicaciones que se muestran en esta tesis, se utiliza el modelo LES que consiste en una viscosidad local que se adapta a la pared dentro de una formulación multiescala variable. Para la formulación de flujo de dos fases, se aplica un método de conjunto de niveles conservador para capturar la interfaz entre dos fluidos y se implementa con un esquema de proyección de densidad variable para simular flujos de dos fases incompresibles en mallas no estructuradas. El algoritmo AMR desarrollado en esta tesis se basa en una estructura de datos de quad / octree y mantiene una relación de 1: 2 entre los niveles de refinamiento. En el caso de las mallas tetraédricas, se sigue un criterio geométrico para mantener la calidad de la malla en una base razonable. La estrategia de paralelización consiste principalmente en la creación de elementos de malla en cada subdominio y establece un número de identificación global único, para evitar elementos duplicados. El equilibrio de carga está asegurado en cada iteración de AMR para mantener el rendimiento paralelo del código CFD. Además, se ha desarrollado un algoritmo de multiplicación de malla (MM) para crear mallas grandes, con diferentes tipos de elementos de malla, pero preservando la topología de una malla original más pequeña. Esta tesis se centra en el estudio de flujos turbulentos y flujos de dos fases utilizando un marco AMR. Los casos estudiados para aplicaciones de LES de flujos turbulentos son el flujo alrededor de uno y dos cilindros separados de sección cuadrada, y el flujo alrededor de un modelo de automóvil simplificado. En este contexto, se desarrolla un criterio de refinamiento basado en la física, que consiste en la velocidad residual calculada a partir de una descomposición de escala múltiple de la velocidad instantánea. Este criterio garantiza la adaptación de la malla siguiendo las estructuras vorticales principales y proporcionando una resolución de malla suficiente en las zonas de interés, es decir, separación de flujo, estelas turbulentas y desprendimiento de vórtices. Los casos estudiados para los flujos de dos fases son el DNS de la burbuja impulsada por la gravedad en 2D y 3D, con un enfoque particular en el régimen de oscilación. Además, el uso de AMR tetraédrico se aplica para la simulación numérica de burbujas impulsadas por la gravedad en dominios complejos. En este tema, la metodología se valida en burbujas que ascienden en canales cilíndricos con topología diferente, donde el estudio de estos casos contribuyó a tener una nueva investigación numérica y una visión física en el desarrollo de una burbuja con efectos de pared

Water wave animation via wavefront parameter interpolation

We present an efficient wavefront tracking algorithm for animating bodies of water that interact with their environment. Our contributions include: a novel wavefront tracking technique that enables dispersion, refraction, reflection, and diffraction in the same simulation; a unique multivalued function interpolation method that enables our simulations to elegantly sidestep the Nyquist limit; a dispersion approximation for efficiently amplifying the number of simulated waves by several orders of magnitude; and additional extensions that allow for time-dependent effects and interactive artistic editing of the resulting animation. Our contributions combine to give us multitudes more wave details than similar algorithms, while maintaining high frame rates and allowing close camera zooms

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