Realistically animated fluids can add substantial realism to interactive applications such as virtual surgery simulators or computer games. In this paper we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate fluids with free surfaces. The method is an extension of the SPH-based technique by Desbrun to animate highly deformable bodies. We gear the method towards fluid simulation by deriving the force density fields directly from the Navier-Stokes equation and by adding a term to model surface tension effects. In contrast to Eulerian grid-based approaches, the particle-based approach makes mass conservation equations and convection terms dispensable which reduces the complexity of the simulation. In addition, the particles can directly be used to render the surface of the fluid. We propose methods to track and visualize the free surface using point splatting and marching cubes-based surface reconstruction. Our animation method is fast enough to be used in interactive systems and to allow for user interaction with models consisting of up to 5000 particles.

Figure 1: A silver block catapulting some wooden blocks into an oncoming wall of water. We present the Rigid Fluid method, a technique for animating the interplay between rigid bodies and viscous incompressible fluid with free surfaces. We use distributed Lagrange multipliers to ensure two-way coupling that generates realistic motion for both the solid objects and the fluid as they interact with one another. We call our method the rigid fluid method because the simulator treats the rigid objects as if they were made of fluid. The rigidity of such an object is maintained by identifying the region of the velocity field that is inside the object and constraining those velocities to be rigid body motion. The rigid fluid method is straightforward to implement, incurs very little computational overhead, and can be added as a bridge between current fluid simulators and rigid body solvers. Many solid objects of different densities (e.g., wood or lead) can be combined in the same animation.

Figure 1: Left: A solid stirring smoke runs at interactive rates, two orders of magnitude faster than previously. Middle: Fully coupled rigid bodies of widely varying density, with flow visualized by marker particles. Right: Interactive manipulation of immersed rigid bodies. Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new variational approach which allows robust and accurate solution on relatively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling between fluid and arbitrary solid simulations that always gives a wellposed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the framework with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.

Figure 1: Sample frames captured from our real-time simulation system (approximately 100,000 wave particles) We present a new method for the real-time simulation of fluid surface waves and their interactions with floating objects. The method is based on the new concept of wave particles, which offers a simple, fast, and unconditionally stable approach to wave simulation. We show how graphics hardware can be used to convert wave particles to a height field surface, which is warped horizontally to account for local wave-induced flow. The method is appropriate for most fluid simulation situations that do not involve significant global flow. It is demonstrated to work well in constrained areas, including wave reflections off of boundaries, and in unconstrained areas, such as an ocean surface. Interactions with floating objects are easily integrated by including wave forces on the objects and wave generation due to object motion. Theoretical foundations and implementation details are provided, and experiments demonstrate that we achieve plausible realism. Timing studies show that the method is scalable to allow simulation of wave interaction with several hundreds of objects at real-time rates.

In this paper, we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate blood as a fluid with free surfaces. While SPH was originally designed to simulate astronomical objects, we gear the method towards fluid simulation by deriving the force density fields directly from the Navier-Stokes equation and by adding a term to model surface tension effects. In contrast to Eulerian grid-based approaches, the particle-based approach makes mass conservation equations and convection terms dispensable which reduces the complexity of the simulation.

this dissertation is drawn from the two publications, "Melting and Flowing" [8] and "Rigid Fluid: Animating the Interplay Between Rigid Bodies and Fluid" [7]. I am extremely grateful to my coauthors, Greg Turk, Peter Mucha and Brooks Van Horn, without whose help those articles would not exist

Figure 1: Simulating interactions between fluid and multiple rigid bodies with our approach. 1

Fluid dynamics governed by Navier-Stokes equations is already solved for decades but the recent trend in computer graphics is to modify the simulation such that it easily controllable for the purpose of computer animation or real time fluid animation. In Eulerian approach, fields must be discretized in space, making these techniques inherently mesh-based. Each mesh cell represents an approximation of the infinitesimal volume at a fixed position in space and during the simulation monitors the evaluation of state variables at that location. Our approach is an extension of a well known Marker-and-Cell (MAC) fluid simulation method, within each cell we define density and pressure in center and fluid velocities on the walls separately in each 6 directions. To simulate several fluids, we propose the modification of Volume-of-Fluid (VOF) method enabling us to tract the fluid surface and integrate it into the multiphase-fluid approach. A mixture of fluids is treated as a single fluid having variable density and viscosity. This scheme allows two or more fluids having different densities and viscosities to be simulated simultaneously. We simulate a one-way solid fluid interaction (either solid influences the velocity of the fluid or fluid moves the solid) that requires having fine details in the colliding areas. To cope with this problem we use an unrestricted octree data structure with adaptive mesh refinement technique to enable higher level of detail and solve Navier Stokes equations for multiple fluids. We propose the technique for discretizing the Poisson equation on octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods, while the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging. Finally, we show several fluid flow animations with static obstacles, floating objects colliding each other.

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Abstract—We present an algorithm for creating realistic animations of characters that are swimming through fluids. Our approach combines dynamic simulation with data-driven kinematic motions (motion capture data) to produce realistic animation in a fluid. The interaction of the articulated body with the fluid is performed by incorporating joint constraints with rigid animation and by extending a solid/fluid coupling method to handle articulated chains. Our solver takes as input the current state of the simulation and calculates the angular and linear accelerations of the connected bodies needed to match a particular motion sequence for the articulated body. These accelerations are used to estimate the forces and torques that are then applied to each joint. Based on this approach, we demonstrate simulated swimming results for a variety of different strokes, including crawl, backstroke, breaststroke and butterfly. The ability to have articulated bodies interact with fluids also allows us to generate simulations of simple water creatures that are driven by simple controllers.