Water wave animation via wavefront parameter interpolation

We present an efficient wavefront tracking algorithm for animating bodies of water that interact with their environment. Our contributions include: a novel wavefront tracking technique that enables dispersion, refraction, reflection, and diffraction in the same simulation; a unique multivalued function interpolation method that enables our simulations to elegantly sidestep the Nyquist limit; a dispersion approximation for efficiently amplifying the number of simulated waves by several orders of magnitude; and additional extensions that allow for time-dependent effects and interactive artistic editing of the resulting animation. Our contributions combine to give us multitudes more wave details than similar algorithms, while maintaining high frame rates and allowing close camera zooms

High-resolution brittle fracture simulation with boundary elements

We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front. Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation. Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix

Putting holes in holey geometry: Topology change for arbitrary surfaces

This paper presents a method for computing topology changes for triangle meshes in an interactive geometric modeling environment. Most triangle meshes in practice do not exhibit desirable geometric properties, so we develop a solution that is independent of standard assumptions and robust to geometric errors. Specifically, we provide the first method for topology change applicable to arbitrary non-solid, non-manifold, non-closed, self-intersecting surfaces. We prove that this new method for topology change produces the expected conventional results when applied to solid (closed, manifold, non-self-intersecting) surfaces---that is, we prove a backwards-compatibility property relative to prior work. Beyond solid surfaces, we present empirical evidence that our method remains tolerant to a variety of surface aberrations through the incorporation of a novel error correction scheme. Finally, we demonstrate how topology change applied to non-solid objects enables wholly new and useful behaviors

ACM Transactions on Graphics

We present a boundary element based method for fast simulation of brittle fracture. By introducing simplifying assumptions that allow us to quickly estimate stress intensities and opening displacements during crack propagation, we build a fracture algorithm where the cost of each time step scales linearly with the length of the crackfront. The transition from a full boundary element method to our faster variant is possible at the beginning of any time step. This allows us to build a hybrid method, which uses the expensive but more accurate BEM while the number of degrees of freedom is low, and uses the fast method once that number exceeds a given threshold as the crack geometry becomes more complicated. Furthermore, we integrate this fracture simulation with a standard rigid-body solver. Our rigid-body coupling solves a Neumann boundary value problem by carefully separating translational, rotational and deformational components of the collision forces and then applying a Tikhonov regularizer to the resulting linear system. We show that our method produces physically reasonable results in standard test cases and is capable of dealing with complex scenes faster than previous finite- or boundary element approaches

A practical method for animating anisotropic elastoplastic materials

This paper introduces a simple method for simulating highly anisotropic elastoplastic material behaviors like the dissolution of fibrous phenomena (splintering wood, shredding bales of hay) and materials composed of large numbers of irregularly‐shaped bodies (piles of twigs, pencils, or cards). We introduce a simple transformation of the anisotropic problem into an equivalent isotropic one, and we solve this new “fictitious” isotropic problem using an existing simulator based on the material point method. Our approach results in minimal changes to existing simulators, and it allows us to re‐use popular isotropic plasticity models like the Drucker‐Prager yield criterion instead of inventing new anisotropic plasticity models for every phenomenon we wish to simulate

ACM Transactions on Graphics

When aiming to seamlessly integrate a fluid simulation into a larger scenario (like an open ocean), careful attention must be paid to boundary conditions. In particular, one must implement special "non-reflecting" boundary conditions, which dissipate out-going waves as they exit the simulation. Unfortunately, the state of the art in non-reflecting boundary conditions (perfectly-matched layers, or PMLs) only permits trivially simple inflow/outflow conditions, so there is no reliable way to integrate a fluid simulation into a more complicated environment like a stormy ocean or a turbulent river. This paper introduces the first method for combining nonreflecting boundary conditions based on PMLs with inflow/outflow boundary conditions that vary arbitrarily throughout space and time. Our algorithm is a generalization of stateof- the-art mean-flow boundary conditions in the computational fluid dynamics literature, and it allows for seamless integration of a fluid simulation into much more complicated environments. Our method also opens the door for previously-unseen postprocess effects like retroactively changing the location of solid obstacles, and locally increasing the visual detail of a pre-existing simulation

Fundamental solutions for water wave animation

This paper investigates the use of fundamental solutions for animating detailed linear water surface waves. We first propose an analytical solution for efficiently animating circular ripples in closed form. We then show how to adapt the method of fundamental solutions (MFS) to create ambient waves interacting with complex obstacles. Subsequently, we present a novel wavelet-based discretization which outperforms the state of the art MFS approach for simulating time-varying water surface waves with moving obstacles. Our results feature high-resolution spatial details, interactions with complex boundaries, and large open ocean domains. Our method compares favorably with previous work as well as known analytical solutions. We also present comparisons between our method and real world examples

Liquid surface tracking with error compensation

Our work concerns the combination of an Eulerian liquid simulation with a high-resolution surface tracker (e.g. the level set method or a Lagrangian triangle mesh). The naive application of a high-resolution surface tracker to a low-resolution velocity field can produce many visually disturbing physical and topological artifacts that limit their use in practice. We address these problems by defining an error function which compares the current state of the surface tracker to the set of physically valid surface states. By reducing this error with a gradient descent technique, we introduce a novel physics-based surface fairing method. Similarly, by treating this error function as a potential energy, we derive a new surface correction force that mimics the vortex sheet equations. We demonstrate our results with both level set and mesh-based surface trackers

A dimension-reduced pressure solver for liquid simulations

This work presents a method for efficiently simplifying the pressure projection step in a liquid simulation. We first devise a straightforward dimension reduction technique that dramatically reduces the cost of solving the pressure projection. Next, we introduce a novel change of basis that satisfies free-surface boundary conditions exactly, regardless of the accuracy of the pressure solve. When combined, these ideas greatly reduce the computational complexity of the pressure solve without compromising free surface boundary conditions at the highest level of detail. Our techniques are easy to parallelize, and they effectively eliminate the computational bottleneck for large liquid simulations

ACM Transactions on Graphics

This paper presents a liquid simulation technique that enforces the incompressibility condition using a stream function solve instead of a pressure projection. Previous methods have used stream function techniques for the simulation of detailed single-phase flows, but a formulation for liquid simulation has proved elusive in part due to the free surface boundary conditions. In this paper, we introduce a stream function approach to liquid simulations with novel boundary conditions for free surfaces, solid obstacles, and solid-fluid coupling. Although our approach increases the dimension of the linear system necessary to enforce incompressibility, it provides interesting and surprising benefits. First, the resulting flow is guaranteed to be divergence-free regardless of the accuracy of the solve. Second, our free-surface boundary conditions guarantee divergence-free motion even in the un-simulated air phase, which enables two-phase flow simulation by only computing a single phase. We implemented this method using a variant of FLIP simulation which only samples particles within a narrow band of the liquid surface, and we illustrate the effectiveness of our method for detailed two-phase flow simulations with complex boundaries, detailed bubble interactions, and two-way solid-fluid coupling