This thesis presents a method to implement a hybrid particle/grid uid simulation on graphics hardware. The goal is to speed up the simulation by exploiting the parallelism of the graphics processing unit, or GPU. The Fluid Implicit Particle method is adapted to the programming style of the GPU. The methods were implemented on a current generation graphics card. The GPU based program exhibited a small speedup over its CPU based counterpart.

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Physical simulations of natural phenomena usually boil down to solving an ordinary or partial differential equation system. Partial differential equation systems can be formulated either in differential form or in integral form. This dissertation explores integral methods for the simulation of magnetic fluids, so-called ferrofluids, and the surface of the vast ocean. The first two parts of this dissertation aim to contribute to the development of accurate and efficient methods for simulating ferrofluids on the macroscopic (in the order of millimeters) scale. The magnetic nature of these fluids imposes challenges for the simulation. The two most important challenges are to first model the influence of ferrofluids on surrounding magnetic fields and second the influence of magnetic forces on the fluids’ dynamics. To tackle these challenges, two Lagrangian simulation methods have been proposed. The first method discretizes the magnetic substance as clusters of particles carrying radial basis functions and applies magnetic forces between these particles. This is a mesh-free method suitable for particle-based fluid simulation frameworks such as smoothed-particle hydrodynamics. The second method follows another direction, only discretizing the fluid’s surface as triangles and vertices. A surface-based simulation for the fluid part is employed, and a boundary element method is utilized for the magnetic part. The magnetic forces are added as gradients of the magnetic energy defined on the fluid’s surface. The second approach has to solve significantly fewer unknowns in the underlying equations, and uses a more accurate surface tension model compared to the radial basis function approach. The proposed methods are able to reproduce a series of characteristic phenomena of magnetic fluids, both qualitatively and in some cases even quantitatively which leads to a better understanding of such kind of materials. The boundary element method employed in the second part shows advantages beyond ferrofluids. In the third part of this thesis, a boundary element method is coupled with a particle-based fluid simulator for ocean simulation. The wavy motion of the ocean is simulated using large triangle meshes, while water splashes are simulated using particles. This approach is much more efficient in terms of computation time and memory consumption.

We present a novel method for example-based simulation of fluid flow. We reconstruct fluid animation from physically based fluid simulation examples. Our framework shows how to decompose a given series of fluid motion example data into small units and then recompose them. We capture the properties of local fluid behavior by dicing the fluid motion example data into sequences of fragments, which have smaller volume and shorter length. We build a database out of these fragments, and propose a matching strategy to generate new fluid animation. To achieve highly efficient database query, we project our fragments onto lower dimensional subspace using Principal Component Analysis (PCA) approach, and construct our data structure as a kd-tree by treating each fragment as a point in this subspace. Our method has been implemented in synthesizing both two-dimensional (2D) and three-dimensional (3D) fluid’s velocity fields.

Fluid simulations for computer graphics applications have attracted the attention of many researchers and practitioners due to the enhanced realism that natural phenomena simulation adds to graphical applications. Vortex methods are receiving increasing attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. However, vortex methods have not been developed yet to the level of other techniques for fluid simulation in computer graphics. In this work we present a novel simulation framework to model inviscid flows using Lagrangian vortex particle methods. We introduce novel stable methods to solve the vorticity flow equations that produce highly detailed visual fluid simulations. We incorporate the full interplay of solids and fluids in our framework. The coupling between free-form solids, represented by arbitrary surface meshes and fluids simulated with vortex methods, leads to visually rich simulations. Previous vortex simulators only focus on modeling the solid as a boundary for the flow. We model solid boundaries using an extended potential flow at the solid surface coupled with a boundary layer simulation. This allows the accurate simulation of two processes of visual interest. The first is the introduction of surface vorticity in the main flow as turbulence (vortex shedding). The second is the motion of the solid induced by fluid forces, which is calculated from the dynamics of vorticity in the flow and the rate of vorticity creation at solid surfaces. We demonstrate high quality results of our methods simulating flows around solid objects and solid object propulsion due to flows. This work ameliorates one of the important omissions in the development of vortex methods for computer graphics, which is the simulation of two-way coupling of solids and fluids.

We present a novel method for example-based simulation of fluid flow. We reconstruct fluid animation from physically based fluid simulation examples. Our framework shows how to decompose a given series of fluid motion example data into small units and then recompose them. We capture the properties of local fluid behavior by dicing the fluid motion example data into sequences of fragments, which have smaller volume and shorter length. We build a database out of these fragments, and propose a matching strategy to generate new fluid animation. To achieve highly efficient database query, we project our fragments onto lower dimensional subspace using Principal Component Analysis (PCA) approach, and construct our data structure as a kd-tree by treating each fragment as a point in this subspace. Our method has been implemented in synthesizing both two-dimensional (2D) and three-dimensional (3D) fluid’s velocity fields.

I propose a particle-based technique for simulating incompressible uid that includes adaptive re nement of particle sampling. Each particle represents a mass of uid in its local region. Particles are split into several particles for ner sampling in regions of complex ow. In regions of smooth ow, neghboring particles can be merged. Depth below the surface and Reynolds number are exploited as our criteria for determining whether splitting or merging should take place. For the uid dynamics calculations, I use the hybrid FLIP method, which is computationally simple and e cient. Since the uid is incompressible, each particle has a volume proportional to its mass. A kernel function, whose e ective range is based on this volume, is used for transferring and updating the particle's physical properties such as mass and velocity. In addition, the particle sampling technique is extended to a fully adaptive approach, supporting adaptive splitting and merging of uid particles and adaptive spatial sampling for the reconstruction of the velocity and pressure elds. Particle splitting allows a detailed sampling of uid momentum in regions of complex ow. Particle merging, in regions of smooth ow, reduces memory and computational overhead. An octree structure is used to compute inter-particle interactions and to compute the pressure eld. The octree supporting eld-based calculations is adapted to provide a ne spatial reconstruction where particles are small and a coarse reconstruction where particles are large. This scheme places computational resources where they are most needed, to handle both ow and surface complexity. Thus, incompressibility can be enforced even in very small, but highly turbulent areas. Simultaneously, the level of detail is very high in these areas, allowing the direct support of tiny splashes and small-scale surface tension e ects. This produces a nely detailed and realistic representation of surface motion.

This thesis work presents a new algorithm for simulating fluid based on the Navier-Stokes equations. The algorithm is designed for cell based sandbox games where interactivity and performance are the main priorities. The algorithm enforces mass conservation conservatively instead of enforcing a divergence free velocity field. A global scale pressure model that simulates hydrostatic pressure is used where the pressure propagates between neighboring cells. A prefix sum algorithm is used to only compute work areas that contain fluid.

Fluid simulations for computer graphics applications have attracted the attention of many researchers and practitioners due to the enhanced realism that natural phenomena simulation adds to graphical applications. Vortex methods are receiving increasing attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. However, vortex methods have not been developed yet to the level of other techniques for fluid simulation in computer graphics. In this work we present a novel simulation framework to model inviscid flows using Lagrangian vortex particle methods. We introduce novel stable methods to solve the vorticity flow equations that produce highly detailed visual fluid simulations. We incorporate the full interplay of solids and fluids in our framework. The coupling between free-form solids, represented by arbitrary surface meshes and fluids simulated with vortex methods, leads to visually rich simulations. Previous vortex simulators only focus on modeling the solid as a boundary for the flow. We model solid boundaries using an extended potential flow at the solid surface coupled with a boundary layer simulation. This allows the accurate simulation of two processes of visual interest. The first is the introduction of surface vorticity in the main flow as turbulence (vortex shedding). The second is the motion of the solid induced by fluid forces, which is calculated from the dynamics of vorticity in the flow and the rate of vorticity creation at solid surfaces. We demonstrate high quality results of our methods simulating flows around solid objects and solid object propulsion due to flows. This work ameliorates one of the important omissions in the development of vortex methods for computer graphics, which is the simulation of two-way coupling of solids and fluids.

We present a novel method for example-based simulation of fluid flow. We reconstruct fluid animation from physically based fluid simulation examples. Our framework shows how to decompose a given series of fluid motion example data into small units and then recompose them. We capture the properties of local fluid behavior by dicing the fluid motion example data into sequences of fragments, which have smaller volume and shorter length. We build a database out of these fragments, and propose a matching strategy to generate new fluid animation. To achieve highly efficient database query, we project our fragments onto lower dimensional subspace using Principal Component Analysis (PCA) approach, and construct our data structure as a kd-tree by treating each fragment as a point in this subspace. Our method has been implemented in synthesizing both two-dimensional (2D) and three-dimensional (3D) fluid’s velocity fields.