Simulation-related papers from Symposium on Computer Animation 2016:
Rahul Narain, Matthew Overby, George E. Brown
We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general-purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constitutive models and hard constraints while retaining the speed, parallelizability, and robustness of projective dynamics. We demonstrate these benefits on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity.
ADMM ⊇ Projective Dynamics: Fast Simulation of General Constitutive Models
Dan Koschier, Crispin Deul, Jan Bender
In this paper we propose a novel method to construct hierarchical $hp$-adaptive Signed Distance Fields (SDFs). We discretize the signed distance function of an input mesh using piecewise polynomials on an axis-aligned hexahedral grid. Besides spatial refinement based on octree subdivision to refine the cell size (h), we hierarchically increase each cell’s polynomial degree (p) in order to construct a very accurate but memory-efficient representation. Presenting a novel criterion to decide whether to apply h- or p-refinement, we demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption than previous approaches. Finally, we demonstrate the usage of our representation as collision detector for geometrically highly complex solid objects in the application area of physically-based simulation.
Hierarchical hp-Adaptive Signed Distance Fields
Aviv Segall, Orestis Vantzos, Mirela Ben-Chen
Hele-Shaw flow describes the slow flow of a viscous liquid between two parallel plates separated by a small gap. In some configurations such a flow generates instabilities known as Saffman-Taylor fingers, which form intricate visual patterns. While these patterns have been an inspiration for artists, as well as thoroughly analyzed by mathematicians, efficiently simulating them remains challenging. The main difficulty involves efficiently computing a harmonic function on a time-varying planar domain, a problem which has been recently addressed in the shape deformation literature using a complex-variable formulation of generalized barycentric coordinates. We propose to leverage similar machinery, and show how the model equations for the Hele-Shaw flow can be formulated in this framework. This allows us to efficiently simulate the flow, while allowing interactive user control of the behavior of the fingers. We additionally show that complex barycentric coordinates are applicable to the exterior domain, and use them to simulate two-phase flow, yielding a variety of interesting patterns.
Hele-Shaw Flow Simulation with Interactive Control using Complex Barycentric Coordinates
Vinicius C. Azevedo, Christopher Batty, Manuel M. Oliveira
Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.
Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps
Xiao Yan, Yun-Tao Jiang, Chen-Feng Li, Ralph R. Martin, and Shi-Min Hu
This work extends existing multiphase-fluid SPH frameworks to cover solid phases, including deformable bodies and granular materials. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. The dynamics of the multiphase system is governed by conservation of mass and momentum within different phases. The behavior of individual phases and the interactions between them are represented by corresponding constitutive laws, which are functions of the volume fraction fields and the velocity fields. Our generalized multiphase SPH framework does not require separate equations for specific phases or tedious interface tracking. As the distribution, shape and motion of each phase is represented and resolved in the same way, the proposed approach is robust, efficient and easy to implement. Various simulation results are presented to demonstrate the capabilities of our new multiphase SPH framework, including deformable bodies, granular materials, interaction between multiple fluids and deformable solids, flow in porous media, and dissolution of deformable solids.
Multiphase SPH Simulation for Interactive Fluids and Solids
Camille Schreck, Damien Rohmer, Stefanie Hahmann, Marie-Paule Cani, Shuo Jin, Charlie Wang, Jean-Francois Bloch
We present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically-based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations.
Non-smooth developable geometry for interactively animating paper crumpling
Albert Chern, Felix Knoppel, Ulrich Pinkall, Peter Schröder, Steffen Weissmann
We describe a new approach for the purely Eulerian simulation of incompressible fluids. In it, the fluid state is represented by a ℂ²-valued wave function evolving under the Schrödinger equation subject to incompressibility constraints. The underlying dynamical system is Hamiltonian and governed by the kinetic energy of the fluid together with an energy of Landau-Lifshitz type. The latter ensures that dynamics due to thin vortical structures, all important for visual simulation, are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. Our implementation uses a simple splitting method for time integration, employing the FFT for Schrödinger evolution as well as constraint projection. Using a standard penalty method we also allow arbitrary obstacles. The resulting algorithm is simple, unconditionally stable, and efficient. In particular it does not require any Lagrangian techniques for advection or to counteract the loss of vorticity. We demonstrate its use in a variety of scenarios, compare it with experiments, and evaluate it against benchmark tests. A full implementation is included in the ancillary materials.
Morten Bojsen-Hansen, Chris Wojtan
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 non-reflecting boundary conditions based on PMLs with inflow/outflow boundary conditions that vary arbitrarily throughout space and time. Our algorithm is a generalization of state-of-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 post-process effects like retroactively changing the location of solid obstacles, and locally increasing the visual detail of a pre-existing simulation.
Generalized Non-Reflecting Boundaries for Fluid Re-Simulation
Ben Jones, Nils Thuerey, Tamar Shinar, Adam W. Bargteil
Physics-based animation is often used to animate scenes containing destruction of near-rigid, man-made materials. For these applications, the most important visual features are plastic deformation and fracture. Methods based on continuum mechanics model these materials as elastoplastic, and must perform expensive elasticity computations even though elastic deformations are imperceptibly small for rigid materials. We introduce an example-based plasticity model based on linear blend skinning that allows artists to author simulation objects using familiar tools. Dynamics are computed using an unmodified rigid body simulator, making our method computationally efficient and easy to integrate into existing pipelines. We introduce a flexible technique for mapping impulses computed by the rigid body solver to local, example-based deformations. For completeness, our method also supports prescoring based fracture. We demonstrate the practicality of our method by animating a variety of destructive scenes.
Example-Based Plastic Deformation of Rigid Bodies