In this paper, we present a simple method for animating natural phenomena such as erosion, sedimentation, and acidic corrosion. We discretize the appropriate physical or chemical equations using finite differences, and we use the results to modify the shape of a solid body. We remove mass from an object by treating its surface as a level set and advecting it inward, and we deposit the chemical and physical byproducts into simulated fluid. Similarly, our technique deposits sediment onto a surface by advecting the level set outward. Our idea can be used for off-line high quality animations as well as interactive applications such as games, and we demonstrate both in this paper.
Category: Fluids
Fast Fluid Simulation using Residual Distribution Schemes
We present a fast method for physically-based animation of fluids on adaptive, unstructured meshes. Our algorithm is capable of correctly handling large-scale fluid forces, as well as their interaction with elastic objects. Our adaptive mesh representation can resolve boundary conditions accurately while maintaining a high level of
efficiency.
Solving General Shallow Wave Equations on Surfaces
We propose a new framework for solving General Shallow Wave Equations (GSWE) in order to efficiently simulate
water flows on solid surfaces under shallow wave assumptions. Within this framework, we develop implicit
schemes for solving the external forces applied to water, including gravity and surface tension. We also present a
two-way coupling method to model interactions between fluid and floating rigid objects. Water flows in this system
can be simulated not only on planar surfaces by using regular grids, but also on curved surfaces directly without
surface parametrization. The experiments show that our system is fast, stable, physically sound, and straightforward
to implement on both CPUs and GPUs. It is capable of simulating a variety of water effects including:
shallow waves, water drops, rivulets, capillary events and fluid/floating rigid body coupling. Because the system
is fast, we can also achieve real-time water drop control and shape design.
Stable Advection-Reaction-Diffusion Systems
Turing first theorized that many biological patterns arise through the processes of reaction and diffusion. Subsequently, reaction-diffusion systems have been studied in many fields, including computer graphics. We first show that for visual simulation purposes, reaction-diffusion equations can be made unconditionally stable using a variety of straightforward methods. Second, we propose an anisotropy embedding that significantly expands the space of possible patterns that can be generated. Third, we show that by adding an advection term, the simulation can be coupled to a fluid simulation to produce visually appealing flows. Fourth, we couple fast marching methods to our anisotropy embedding to create a painting interface to the simulation. Unconditional stability to maintained throughout, and our system runs at interactive rates. Finally, we show that on the Cell processor, it is possible to implement reaction-diffusion on top of an existing fluid solver with no significant performance impact.
Efficient Refinement of Dynamic Point Data
Particle simulations as well as geometric modeling techniques have demonstrated their ability to process and render points interactively. However, real-time particle-based fluid simulations suffer from poor rendering quality due to low surface particle resolutions. Surfaces appear blobby, surface details are lost, and features like edges are degraded due to smoothing effects. This paper presents a novel point refinement method for irregularly sampled, dynamic points coming from a particle-based fluid simulation. Our interpolation algorithm can handle complex geometries including splashes, and at the same time preserves features like edges. Point collisions are avoided resulting in a nearly uniform sampling facilitating surface reconstruction techniques. No point preprocessing is necessary, and point neighborhoods are dynamically updated reducing computation and memory costs. We show that our algorithm can efficiently detect and refine the surface points of a fluid and we demonstrate the improvement of rendering quality and applicability to real-time simulations.
A Simple Boiling Module
Recent efforts to visually capture the phenomena of boiling have proposed monolithic approaches that extend the basic techniques underlying existing fluid solvers. In this work, we show that if we instead treat boiling as a separate computational module to be loosely coupled to an existing solver, a very easy to implement, highly efficient algorithm can be designed that produces excellent visual results, even on coarse (64^3) grids. The algorithm is also highly SIMD-amenable, allowing the boiling computation to be farmed out to a GPU or Playstation 3 Cell processor. Our algorithm takes less than 100 lines of commented, readable C++, and can be integrated into an existing particle level set fluid solver with virtually no modifications. A serial implementation consumes between 3-5% of the overall running time, and a preliminary SIMD implementation shows that a 64^3 simulation runs at 130 FPS, making the computational cost of the module totally negligible.
Animation of Chemically Reactive Fluids using a Hybrid Simulation Method
Chemical phenomena abound in the real world, and often comprise indispensable elements of visual effects that are routinely created in the film industry. In this paper, we present a hybrid technique for simulating chemically reactive fluids, based on the theory of chemical kinetics. Our method makes synergistic use of both Eulerian grid-based methods and Lagrangian particle methods to simulate real and hypothetical chemical mechanisms effectively and efficiently. We demonstrate that by modeling chemical reactions using a particle system, an established, physically based fluid system can be extended easily to generate a wide range of chemical phenomena, ranging from catalysis and erosion to fire and explosions, with only a small additional cost.
Animation of Chemically Reactive Fluids Using a Hybrid Simulation Method
Real-time Simulations of Bubbles and Foam within a Shallow-Water Framework
Bubbles and foam are important fluid phenomena on scales that we encounter in our lives every day. While different techniques to handle these effects were developed in the past years, they require a full 3D fluid solver with free surfaces and surface tension. We present a shallow water based particle model that is coupled with a smoothed particle hydrodynamics simulation to demonstrate that real-time simulations of bubble and foam effects are possible with high frame rates. A shallow water simulation is used to represent the overall water volume. It is coupled to a particle-based bubble simulation with a flow field of spherical vortices. This bubble simulation is interacting with a smoothed particle hydrodynamics simulation including surface tension to handle foam on the fluid surface. The realism and performance of our approach is demonstrated with several test cases that run with high frame rates on a standard PC.
Real-time Simulations of Bubbles and Foam within a Shallow-Water Framework
Legendre Fluids: A Unified Framework for Analytic Reduced Space Modeling and Rendering of Participating Media
In this paper, we present a unified framework for reduced space modeling and rendering of dynamic and nonhomogenous participating media, like snow, smoke, dust and fog. The key idea is to represent the 3D spatial variation of the density, velocity and intensity fields of the media using the same analytic basis. In many situations, natural effects such as mist, outdoor smoke and dust are smooth (low frequency) phenomena, and can be compactly represented by a small number of coefficients of a Legendre polynomial basis. We derive analytic expressions for the derivative and integral operators in the Legendre coefficient space, as well as the triple product integrals of Legendre polynomials. These mathematical results allow us to solve both the Navier-Stokes equations for fluid flow and light transport equations for single scattering efficiently in the reduced Legendre space. Since our technique does not depend on volume grid resolution, we can achieve computational speedups as compared to spatial domain methods while having low memory and pre-computation requirements as compared to datadriven approaches. Also, analytic definition of derivatives and integral operators in the Legendre domain avoids the approximation errors inherent in spatial domain finite difference methods. We demonstrate many interesting visual effects resulting from particles immersed in fluids as well as volumetric scattering in non-homogenous and dynamic participating media, such as fog and mist.
Screen Space Meshes
We present a simple yet powerful approach for the generation and rendering of surfaces defined by the boundary of a three-dimensional point cloud. First, a depth map plus internal and external silhouettes of the surface are generated in screen space. These are used to construct a 2D screen space triangle mesh with a new technique that is derived from Marching Squares. The resulting mesh is transformed back to 3D world space for the computation of occlusions, reflections, refraction, and other shading effects. One of the main applications for screen space meshes is the visualization of Lagrangian, particle-based fluids models. Our new method has several advantages over the full 3D Marching Cubes approach. The algorithm only generates surface where it is visible, view-dependent level of detail comes for free, and interesting visual effects are possible by filtering in screen space.