Divergence-Free Smoothed Particle Hydrodynamics

Jan Bender, Dan Koschier

In this paper we introduce an efficient and stable implicit SPH method for the physically-based simulation of incompressible fluids. In the area of computer graphics the most efficient SPH approaches focus solely on the correction of the density error to prevent volume compression. However, the continuity equation for incompressible flow also demands a divergence-free velocity field which is neglected by most methods. Although a few methods consider velocity divergence, they are either slow or have a perceivable density fluctuation. Our novel method uses an efficient combination of two pressure solvers which enforce low volume compression (below 0.01%) and a divergence-free velocity field. This can be seen as enforcing incompressibility both on position level and velocity level. The first part is essential for realistic physical behavior while the divergence-free state increases the stability significantly and reduces the number of solver iterations. Moreover, it allows larger time steps which yields a considerable performance gain since particle neighborhoods have to be updated less frequently. Therefore, our divergence-free SPH (DFSPH) approach is significantly faster and more stable than current state-of-the-art SPH methods for incompressible fluids. We demonstrate this in simulations with millions of fast moving particles.

Divergence-Free Smoothed Particle Hydrodynamics

Functional Thin Films on Surfaces

Omri Azencot, Orestis Vantzos, Max Wardetzky, Martin Rumpf, Mirela Ben-Chen

The motion of a thin viscous film of fluid on a curved surface exhibits many intricate visual phenomena, which are challenging to simulate using existing techniques. A possible alternative is to use a reduced model, involving only the temporal evolution of the mass density of the film on the surface. However, in this model, the motion is governed by a fourth-order nonlinear PDE, which involves geometric quantities such as the curvature of the underlying surface, and is therefore difficult to discretize. Inspired by a recent variational formulation for this problem on smooth surfaces, we present a corresponding model for triangle meshes. We provide a discretization for the curvature and advection operators which leads to an efficient and stable numerical scheme, requires a single sparse linear solve per time step, and exactly preserves the total volume of the fluid. We validate our method by qualitatively comparing to known results from the literature, and demonstrate various intricate effects achievable by our method, such as droplet formation, evaporation, droplets interaction and viscous fingering.

Functional Thin Films on Surfaces

Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail

Richard Malgat, Benjamin Gilles, David I.W. Levin, Mathieu Nesme, Francois Faure

We present a new framework for artist driven level of detail in solid simulations. Simulated objects are simultaneously embedded in several, separately designed deformation models with their own independent degrees of freedom. The models are ordered to apply their deformations hierarchically, and we enforce the uniqueness of the dynamics solutions using a novel kinetic filtering operator designed to ensure that each child only adds detail motion to its parent without introducing redundancies. This new approach allows artists to easily add fine-scale details without introducing unnecessary degrees-of-freedom to the simulation or resorting to complex geometric operations like anisotropic volume meshing. We illustrate the utility of our approach with several detail enriched simulation examples.

Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail

SCA 2015

Symposium on Computer Animation, 2015 edition: Illuminating Ideas!

LazyFluids: Appearance Transfer for Fluid Animations

Ondrej Jamriska, Jakub Fiser, Paul Asente, Jingwan Lu, Eli Shechtman, Daniel Sykora

In this paper we present a novel approach to appearance transfer for fluid animations based on flow-guided texture synthesis. In contrast to common practice where pre-captured sets of fluid elements are combined in order to achieve desired motion and look, we bring the possibility of fine-tuning motion properties in advance using CG techniques, and then transferring the desired look from a selected appearance exemplar. We demonstrate that such a practical workflow cannot be simply implemented using current state-of-the-art techniques, analyze what the main obstacles are, and propose a solution to resolve them. In addition, we extend the algorithm to allow for synthesis with rich boundary effects and video exemplars. Finally, we present numerous results that demonstrate the versatility of the proposed approach.

LazyFluids: Appearance Transfer for Fluid Animations

Nonlinear Material Design Using Principal Stretches

Hongyi Xu, Funshing Sin, Yufeng Zhu, Jernej Barbic

The Finite Element Method is widely used for solid deformable object simulation in film, computer games, virtual reality and medicine. Previous applications of nonlinear solid elasticity employed materials from a few standard families such as linear corotational, nonlinear St.Venant-Kirchhoff, Neo-Hookean, Ogden or Mooney-Rivlin materials. However, the spaces of all nonlinear isotropic and anisotropic materials are infinite-dimensional and much broader than these standard materials. In this paper, we demonstrate how to intuitively explore the space of isotropic and anisotropic nonlinear materials, for design of animations in computer graphics and related fields. In order to do so, we first formulate the internal elastic forces and tangent stiffness matrices in the space of the principal stretches of the material. We then demonstrate how to design new isotropic materials by editing a single stress-strain curve, using a spline interface. Similarly, anisotropic (orthotropic) materials can be designed by editing three curves, one for each material direction. We demonstrate that modifying these curves using our proposed interface has an intuitive, visual, effect on the simulation. Our materials accelerate simulation design and enable visual effects that are difficult or impossible to achieve with standard nonlinear materials.

Nonlinear Material Design Using Principal Stretches

An Implicit Viscosity Formulation for SPH Fluids

Andreas Peer, Markus Ihmsen, Jens Cornelis, Matthias Teschner

We present a novel implicit formulation for highly viscous fluids simulated with Smoothed Particle Hydrodynamics SPH. Compared to explicit methods, our formulation is significantly more efficient and handles a larger range of viscosities. Differing from existing implicit formulations, our approach reconstructs the velocity field from a target velocity gradient. This gradient encodes a desired shear-rate damping and preserves the velocity divergence that is introduced by the SPH pressure solver to counteract density deviations. The target gradient ensures that pressure and viscosity computation do not interfere. Therefore, only one pressure projection step is required, which is in contrast to state-of-the-art implicit Eulerian formulations. While our model differs from true viscosity in that vorticity diffusion is not encoded in the target gradient, it nevertheless captures many of the qualitative behaviors of viscous liquids. Our formulation can easily be incorporated into complex scenarios with one- and two-way coupled solids and multiple fluid phases with different densities and viscosities.

An Implicit Viscosity Formulation for SPH Fluids

Fluid Volume Modeling from Sparse Multi-view Images by Appearance Transfer

Makoto Okabe, Yoshinori Dobashi, Ken Anjyo, Rikio Onai

We propose a method of three-dimensional (3D) modeling of volumetric fluid phenomena from sparse multi-view images (e.g., only a single-view input or a pair of front- and side-view inputs). The volume determined from such sparse inputs using previous methods appears blurry and unnatural with novel views; however, our method preserves the appearance of novel viewing angles by transferring the appearance information from input images to novel viewing angles. For appearance information, we use histograms of image intensities and steerable coefficients. We formulate the volume modeling as an energy minimization problem with statistical hard constraints, which is solved using an expectation maximization (EM)-like iterative algorithm. Our algorithm begins with a rough estimate of the initial volume modeled from the input images, followed by an iterative process whereby we first render the images of the current volume with novel viewing angles. Then, we modify the rendered images by transferring the appearance information from the input images, and we thereafter model the improved volume based on the modified images. We iterate these operations until the volume converges. We demonstrate our method successfully provides natural-looking volume sequences of fluids (i.e., fire, smoke, explosions, and a water splash) from sparse multi-view videos. To create production-ready fluid animations, we further propose a method of rendering and editing fluids using a commercially available fluid simulator.
Fluid Volume Modeling from Sparse Multi-view Images by Appearance Transfer

Stable Constrained Dynamics

Maxime Tournier, Matthieu Nesme, Benjamin Gilles, Francois Faure

We present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers.

Stable Constrained Dynamics

High-Resolution Brittle Fracture Simulation with Boundary Elements

David Hahn, Chris Wojtan

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.

High-Resolution Brittle Fracture Simulation with Boundary Elements