Physics-Based Animation

Kenny Erleben, Marek Misztal, J. Andreas Baerentzen

We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to be able to handle advection in a numerically simple Lagrangian approach. Following this a finite element method is used for the remaining terms of the fractional step method. The key to deriving a discretization for the diffusion forces lies in restating the momentum equations in terms of a Newtonian stress tensor. Rather than applying a straightforward temporal finite difference method followed by a projection method to enforce incompressibility as done in the stable fluids method, the last step of the fractional step method is rewritten as an optimization problem to make it easy to incorporate non-linear force terms such as surface tension.

Mathematical Foundation of the Optimization-Based Fluid Animation Method

Genichi Kawada, Takashi Kanai

We propose a method to procedurally model the fluid flows of explosion phenomena by taking physical properties into account. Explosion flows are always quite difficult to control, because they easily disturb each other and change rapidly. With this method, the target flows are described by control paths, and the propagation flows are controlled by following these paths. We consider the physical properties, which are the propagations of the pressure generated by the ignition, the detonation state caused by the pressure and the fuel combustions. Velocity, density, temperature and pressure fields are generated procedurally, and the fluid flows are computed from these four fields based on grid-based fluid simulations. Using this method, we can achieve a fluid motion that closely resembles one generated solely through simulation. This method realizes the modeling of flows controlled frame by frame and follows the flow’s physical properties.

Procedural Fluid Modeling of Explosion Phenomena Based on Physical Properties

Christopher Batty, Ben Houston

We present the first spatially adaptive Eulerian fluid animation method to support challenging viscous liquid effects such as folding, coiling, and variable viscosity. We propose a tetrahedral node-based embedded finite volume method for fluid viscosity, adapted from popular techniques for Lagrangian deformable objects. Applied in an Eulerian fashion with implicit integration, this scheme stably and efficiently supports high viscosity fluids while yielding symmetric positive definite linear systems. To integrate this scheme into standard tetrahedral mesh-based fluid simulators, which store normal velocities on faces rather than velocity vectors at nodes, we offer two methods to reconcile these representations. The first incorporates a mapping between different degrees of freedom into the viscosity solve itself. The second uses a FLIP-like approach to transfer velocity data between nodes and faces before and after the linear solve. The former offers tighter coupling by enabling the linear solver to act directly on the face velocities of the staggered mesh, while the latter provides a sparser linear system and a simpler implementation. We demonstrate the effectiveness of our approach with animations of spatially varying viscosity, realistic rotational motion, and viscous liquid buckling and coiling.

A Simple Finite Volume Method for Adaptive Viscous Liquids

Raphael Diziol, Jan Bender, Daniel Bayer

We introduce an efficient technique for robustly simulating incompressible objects with thousands of elements in real-time. Instead of considering a tetrahedral model, commonly used to simulate volumetric bodies, we simply use their surfaces. Not requiring hundreds or even thousands of elements in the interior of the object enables us to simulate more elements on the surface, resulting in high quality deformations at low computation costs. The elasticity of the objects is robustly simulated with a geometrically motivated shape matching approach which is extended by a fast summation technique for arbitrary triangle meshes suitable for an efficient parallel computation on the GPU. Moreover, we present an oscillation-free and collision-aware volume constraint, purely based on the surface of the incompressible body. The novel heuristic we propose in our approach enables us to conserve the volume, both globally and locally. Our volume constraint is not limited to the shape matching method and can be used with any method simulating the elasticity of an object. We present several examples which demonstrate high quality volume conserving deformations and compare the run-times of our CPU implementation, as well as our GPU implementation with similar methods.

Robust Real-Time Deformation of Incompressible Surface Meshes

Yubo Zhang, Carlos Correa, Kwan-Liu Ma

We present a novel graph-based data-driven technique for cost-effective fire modeling. This technique allows composing long animation sequences using a small number of short simulations. While traditional techniques such as motion graphs and motion blending work well for character motion synthesis, they cannot be trivially applied to fluids to produce results with physically consistent properties which are crucial to the visual appearance of fluids. Motivated by the motion graph technique used in character animations, we introduce a new type of graph which can be applied to create various fire phenomena. Each graph node consists of a group of compact spatialtemporal flow pathlines instead of a set of volumetric state fields. Consequently, achieving smooth transitions between discontinuous graph nodes for modeling turbulent fires becomes feasible and computationally efficient.The synthesized particle flow results allow direct particle controls which is much more flexible than a full volumetric representation of the simulation output. The accompanying video shows the versatility and potential power of this new technique for synthesizing realtime complex fire at the quality comparable to production animations.

Graph-based Fire Synthesis

The draft program for SCA 2011 is online here. Ke-Sen Huang maintains links to the full set of papers here.  Many of the papers involve physical simulation, including:

• Physics-based Character Skinning using Multi-Domain Subspace Deformations
• A Multigrid Fluid Pressure Solver Handling Separating Solid Boundary Conditions
• Mass and Momentum Conservation for Fluid Simulation
• Mathematical Foundation of the Optimization-Based Fluid Animation Method
• A Simple Finite Volume Method for Adaptive Viscous Liquids
• Procedural Modelling of Explosion Phenomena Based on Physical Properties
• Preview-based Sampling for Controlling Gaseous Simulations
• Graph-based Fire Synthesis
• A Particle-based Method for Preserving Fluid Sheets
• A Level-set Method for Skinning Animated Particle Data
• SPH Granular Flow with Friction and Cohesion
• Hybrid Smoothed Particle Hydrodynamics
• Optimization for Sag-Free Simulations
• Robust Real-Time Deformation of Incompressible Surface Meshes
• Asynchronous Integration with Phantom Meshes
• Element-Wise Mixed Implicit-Explicit Integration for Stable Dynamic Simulation of Deformable Objects

We propose a two-scale method for particle-based fluids that allocates computing resources to regions of the fluid where complex flow behavior emerges. Our method uses a low- and a high-resolution simulation that run at the same time. While in the coarse simulation the whole fluid is represented by large particles, the fine level simulates only a subset of the fluid with small particles. The subset can be arbitrarily defined and also dynamically change over time to capture complex flows and small-scale surface details. The low- and high-resolution simulations are coupled by including feedback forces and defining appropriate boundary conditions. Our method offers the benefit that particles are of the same size within each simulation level. This avoids particle splitting and merging processes, and allows the simulation of very large resolution differences without any stability problems. The model is easy to implement, and we show how it can be integrated into a standard SPH simulation as well as into the incompressible PCISPH solver. Compared to the single-resolution simulation, our method produces similar surface details while improving the efficiency linearly to the achieved reduction rate of the particle number.

Two-Scale Particle Simulation

We present a new algorithm for near-interactive simulation of skeleton driven, high resolution elasticity models. Our methodology is used for soft tissue deformation in character animation. The algorithm is based on a novel discretization of corotational elasticity over a hexahedral lattice. Within this framework we enforce positive definiteness of the stiffness matrix to allow efficient quasistatics and dynamics. In addition, we present a multigrid method that converges with very high efficiency. Our design targets performance through parallelism using a fully vectorized and branch-free SVD algorithm as well as a stable one-point quadrature scheme. Since body collisions, self collisions and soft-constraints are necessary for real-world examples, we present a simple framework for enforcing them. The whole approach is demonstrated in an end-to-end production-level character skinning system.

Efficient Elasticity for Character Skinning with Contact and Collisions

This paper shows a method to extend 3D nonlinear elasticity model reduction to open-loop multi-level reduced deformable structures. Given a volumetric mesh, we decompose the mesh into several subdomains, build a reduced deformable model for each domain, and connect the domains using inertia coupling. This makes model reduction deformable simulations much more versatile: localized deformations can be supported without prohibitive computational costs, parts can be re-used and precomputation times shortened. Our method does not use constraints, and can handle large domain rigid body motion in addition to large deformations, due to our derivation of the gradient and Hessian of the rotation matrix in polar decomposition. We show real-time examples with multi-level domain hierarchies and hundreds of reduced degrees of freedom.

Real-time Large-deformation Substructuring

We present a new Eulerian fluid simulation method, which allows real-time simulations of large scale three dimensional liquids. Such scenarios have hitherto been restricted to the domain of off-line computation. To reduce computation time we use a hybrid grid representation composed of regular cubic cells on top of a layer of tall cells. With this layout water above an arbitrary terrain can be represented without consuming an excessive amount of memory and compute power, while focusing effort on the area near the surface where it most matters. Additionally, we optimized the grid representation for a GPU implementation of the fluid solver. To further accelerate the simulation, we introduce a specialized multigrid algorithm for solving the Poisson equation and propose solver modifications to keep the simulation stable for large time steps. We demonstrate the efficiency of our approach in several real-world scenarios, all running above 30 frames per second on a modern GPU. Some scenes include additional features such as two-way rigid body coupling as well as particle representations of sub-grid detail.

Real-Time Eulerian Water Simulation Using a Restricted Tall Cell Grid