<p>The Particle Level set method is a successful extension to Level set methods to improve thevolume preservation in fluid simulations. This thesis will analyze how sparse volume data structures can be used to store both the signed distance function and the particles in order to improve access speed and memory efficiency. This Particle Level set implementation will be evaluated against Digital Domains current Particle Level set implementation. Different degrees of quantization will be used to implement particle representations with varying accuracy. These particles will be tested and both visual results and error measurments will be presented. The sparse volume data structures DB-Grid and Field3D will be evaluated in terms of speed and memory efficiency.</p>

<p>We present a method for stable buildup of snow on surfaces of</p><p>arbitrary topology and geometric complexity. This is achieved by</p><p>tracing quantities of snow, so-called snow packages,</p><p>through a dynamic wind field. Dual compact level sets are used to</p><p>represent geometry as well as accumulated snow. The level sets</p><p>have also proven to be well suited for the internal boundaries for</p><p>our Navier-Stokes solver, which produces a wind field that changes</p><p>according to snow buildup. Our method is different from previous</p><p>work in that all the addition of snow is done by local operations,</p><p>avoiding computationally expensive global refinement procedures.</p><p>The main contribution of this work is a dual level set method for</p><p>particle interaction with level sets.</p>

In this thesis, we have developed a Subtructured Finite Element / eXtended Finite Element (S-FE/XFE) method. The S-FE/XFE method consists in decomposing the geometry into safe FE-domains and cracked XFE-domains, and solving the interface problem with the Finite Element Tearing and Interconnecting method (FETI).This method allows for handling complex crack configurations in 3D structures with common commercial FE software that do not feature the XFEM. The method is also extended to a mixed dimensional formulation, where the FE-domain is discretised with shell elements while the XFE-domain is modelled with three-dimensional solid elements. This is the so-called S-FE Shell/XFE 3D method. The mixed dimensional formulation is more convenient than a full XFE-3D formulation because it significantly reduces the computational cost and it is more accurate compared to a full shell model because it includes three-dimensional local features such as three-dimensional crack. The compatibility of the displacements through the interface is ensured using the Reissner-Mindlin equation. The method has been extensively validated towards both academic problems and semi-industrial benchmarks in order to demonstrate the benefits of this approach. Among them, the S-FE/XFE method is applied to a crack analysis in a section of a compressor drum of a turbofan engine. The results obtained with the S-FE/XFE method are compared with those obtained with a standard FE computation. Furthermore, two applications of the S-FE shell/XFE 3D approach are proposed. First the load carrying capacity of a section of stiffened panel containing a through-the-thickness crack is investigated (this is the one-bay crack configuration). Second, the ability of the method for handling small surface cracks in large finite element models is addressed by looking at a generic 'large pressure panel' presenting realistic crack configurations.

In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.

This thesis introduces geometric dynamic active contours in the context of visual tracking, augmenting geometric curve evolution with physically motivated dynamics. Adding additional state information to an evolving curve lifts the curve evolution problem to space dimensions larger than two and thus forbids the use of classical level set techniques. This thesis therefore develops and explores level set methods for problems of higher codimension, putting an emphasis on the vector distance function based approach. This formalism is very general, it is interesting in its own right and still a challenging topic. Two different implementations for geometric dynamic active contours are explored: the full level set approach as well as a simpler partial level set approach. The full level set approach results in full topological flexibility and can deal with curve intersections in the image plane. However, it is computationally expensive. On the other hand the partial level set approach gives up the topological flexibility (intersecting curves cannot be represented) for increased computational efficiency. Contours colliding with different dynamic information (e.g., objects crossing in the image plane) will be merged in the partial level set approach whereas they will correctly traverse each other in the full level set approach. Both implementations are illustrated on synthetic and real examples. Compared to the traditional static curve evolution case, fundamentally different evolution behaviors can be obtained by propagating additional information along with every point on a curve.

This project is to explore the manufacturing and processing of laser or electron beam, formed on the surface morphology after curing and processing parts, such as surfacefilled, depression, or the formation of ripples; These reactions will directly affect the surface heat treatment and welding quality of thefinished product This study to consider the mass, momentum and energy equations, the introduction of theinterface and boundary conditions to simulate the real process In order to promote quality stability, and a large amount of production capacity and reduce costs, we must understand the institutions of the reaction In this thesis, the phase field method (Phase-field method) (Two-phase flow) two-phase flow simulation of metal surface by a concentrated source of heat melt the transient heat flow behavior

In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.

This thesis presents a method for simulating fluids on a view dependent grid structure to exploit level-of-detail with distance to the viewer. Current computer graphics techniques, such as the Stable Fluid and Particle Level Set methods, are modified to support a nonuniform simulation grid. In addition, infinite fluid boundary conditions are introduced that allow fluid to flow freely into or out of the simulation domain to achieve the effect of large, boundary free bodies of fluid. Finally, a physically based rendering method known as photon mapping is used in conjunction with ray tracing to generate realistic images of water with caustics. These methods were implemented as a C++ application framework capable of simulating and rendering fluid in a variety of user-defined coordinate systems.

<p>Consider a mixture of two immiscible, incompressible fluids e.g. oil and water. Since the fluids do not mix, an interface between the two fluids will form and move in time. The motion of the two fluids can be modelled by the incompressible Navier-Stokes equations for two phase flow with surface tension together with a representation of the moving interface. The parameters in the Navier-Stokes equations will depend on the position and other properties of the interface. The interface should move with the velocity of the flow at the interface. Since the fluids are incompressible, the density of each fluid is constant. Mass conservation then implies that the volume occupied by each of the two fluids should not change with time. The object of this thesis has been to develop a new numerical method to simulate incompressible two phase flow accurately that conserves mass and volume of each fluid correctly.</p><p>Numerical simulations of incompressible two phase flow with surface tension have been a challenge for many years. Several methods have been developed and used prior to the work presented in this thesis. The two most commonly used methods are volume of fluid methods and level set methods. There are advantages and disadvantages of both of the methods.</p><p>In volume of fluid methods the interface is represented by a discontinuity of a globally defined function. Because of the discontinuity it is hard both to move the interface as well as to calculate properties of the interface such as curvature. Specially designed methods have to be used, and all these methods are low order accurate. Volume of fluid methods do however conserve the volumes of the two fluids correctly.</p><p>In level set methods the interface is represented by the zero contour of the globally defined signed distance function. This function is smooth across the interface. Since the function is smooth, standard methods for partial differential equations can be used to advect the interface accurately. A reinitialization is however needed to make sure that the level set function remains a signed distance function. During this process the zero contour might move slightly. Because of this, the volume conservation of the method becomes poor.</p><p>In this thesis we present a new level set method. The method is designed such that the volume of each fluid is conserved, at least approximately. The interface is represented by the 0.5 contour of a regularized characteristic function. As for standard level set methods, the interface is moved first by an advective step, and then reinitialized. Unlike traditional level set methods, we can formulate the reinitialization as a conservation law. Conservative methods can then be used to move and to reinitialize the level set function numerically. Since the level set function is a regularized characteristic function, we can expect good conservation of the volume bounded by the interface.</p><p>The method is discretized using both finite differences and finite elements. Uniform and adaptive grids are used in both two and three space dimensions. Good convergence as well as volume conservation is observed. Theoretical studies are performed to investigate the conservation and the computational time needed for reinitialization.</p>

L'objectif de cette these est d'evaluer la capacite d'une methode particulaire inspiree des methodes Vortex-In-Cell a simuler les ecoulements de la dynamique des gaz, et plus particulierement les ecoulements multifluides. Dans un premier temps nous developpons une methode particules-grille avec remaillage pour les ecoulements compressibles non-visqueux. Le remaillage, conservatif, est realise avec des fonctions d'interpolation d'ordre eleve. Nous analysons theoriquement et testons numeriquement cette methode. Nous mettons notamment en evidence des liens forts entre notre methode et des schemas aux differences finies d'ordre eleve, de type Lax-Wendroff, et nous proposons un nouveau schema d'advection des particules, simple et plus precis. Puis nous implantons une technique multi-niveaux inspiree de l'AMR. Enfin, nous discretisons une technique de type level-set sur les particules afin de simuler l'interface entre fluides. Nous utilisons la technique multi-niveaux pour resoudre plus precisement l'interface et d'ameliorer la conservation des masses partielles.