Physics-Based Animation

Dan Gerszewski, Ladislav Kavan, Peter-Pike Sloan, Adam W. Bargteil

We present several enhancements to model-reduced fluid simulation that allow improved simulation bases and two-way solid-fluid coupling. Specifically, we present a basis enrichment scheme that allows us to combine data driven or artistically derived bases with more general analytic bases derived from Laplacian Eigenfunctions. We handle two-way solid-fluid coupling in a time-splitting fashion—we alternately timestep the fluid and rigid body simulators, while taking into account the effects of the fluid on the rigid bodies and vice versa. We employ the vortex panel method to handle solid-fluid coupling and use dynamic pressure to compute the effect of the fluid on rigid bodies.

Enhancements to Model-Reduced Fluid Simulation

Florian Ferstl, Rudiger Westermann, Christian Dick

Regular grids are attractive for numerical fluid simulations because they give rise to efficient computational kernels. However, for simulating high resolution effects in complicated domains they are only of limited suitability due to memory constraints. In this paper we present a method for liquid simulation on  an adaptive octree grid using a hexahedral finite element discretization, which reduces memory requirements by coarsening the elements in the interior of the liquid body. To impose free surface boundary conditions with second order accuracy, we incorporate a particular class of Nitsche methods enforcing the Dirichlet boundary conditions for the pressure in a variational sense. We then show how to construct a multigrid hierarchy from the adaptive octree grid, so that a time efficient geometric multigrid solver can be used. To improve solver convergence, we propose a special treatment of liquid boundaries via composite finite elements at coarser scales. We demonstrate the effectiveness of our method for liquid simulations that would require hundreds of millions of simulation elements in a non-adaptive regime.

Large-Scale Liquid Simulation on Adaptive Hexahedral Grids

Xiaowei He, Huamin Wang, Fengjun Zhang, Hongan Wang, Guoping Wang, Kun Zhou

Smoothed particle hydrodynamics (SPH) is efficient, mass preserving, and flexible in handling topological changes. However, small-scale thin features are difficult to simulate in SPH-based free surface flows, due to a number of robustness and stability issues. In this paper, we address this problem from two perspectives: the robustness of surface forces and the numerical instability of thin features. We present a new surface tension force scheme based on a free surface energy functional, under the diffuse interface model. We develop an efficient way to calculate the air pressure force for free surface flows, without using air particles. Compared with previous surface force formulae, our formulae are more robust against particle sparsity in thin feature cases. To avoid numerical instability on thin features, we propose to adjust the internal pressure force by estimating the internal pressure at two scales and filtering the force using a geometry-aware anisotropic kernel. Our result demonstrates the effectiveness of our algorithms in handling a variety of small-scale thin liquid features, including thin sheets, thin jets, and water splashes.

Robust Simulation of Small-Scale Thin Features in SPH-based Free Surface Flows

J. Cornelis, M. Ihmsen, A. Peer, M. Teschner

We propose to use Implicit Incompressible Smoothed Particle Hydrodynamics (IISPH) for pressure projection and boundary handling in Fluid-Implicit-Particle (FLIP) solvers for the simulation of incompressible fluids. This novel combination addresses two issues of existing SPH and FLIP solvers, namely mass preservation in FLIP and efficiency and memory consumption in SPH. First, the SPH component enables the simulation of incompressible fluids with perfect mass preservation. Second, the FLIP component efficiently enriches the SPH component with detail that is comparable to a standard SPH simulation with the same number of particles, while improving the performance by a factor of 7 and significantly reducing the memory consumption. We demonstrate that the proposed IISPH-FLIP solver can simulate incompressible fluids with a quantifiable, imperceptible density deviation
below 0:1%. We show large-scale scenarios with up to 160 million particles that have been processed on a single desktop PC using only 15GB of memory. One- and two-way coupled solids are illustrated.

IISPH-FLIP for Incompressible Fluids

Sara Schvartzmann, Miguel Otaduy

We propose a novel algorithm to simulate brittle fracture. It augments previous methods based on Voronoi diagrams, improving their versatility and their ability to adapt fracture patterns automatically to diverse collision scenarios and object properties. We cast brittle fracture as the computation of a high-dimensional Centroidal Voronoi Diagram (CVD), where the distribution of fracture fragments is guided by the deformation field of the fractured object. By formulating the problem in high dimensions, we support robustly object and crack concavities, as well as intuitive artist control. We further accelerate the fracture animation process with example-based learning of the fracture degree, and a highly parallel tessellation algorithm. As a result, we obtain fast animations of detailed and rich fractures, with fracture patterns that adapt to each particular collision scenario.

Fracture animation based on high-dimensional Voronoi diagrams

Stefan Auer, Rudiger Westermann

We present an Eulerian method for the real-time simulation of intrinsic fluid dynamics effects on deforming
surfaces. Our method is based on a novel semi-Lagrangian closest point method for the solution of partial
differential equations on animated triangle meshes.We describe this method and demonstrate its use to com-
pute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying
our technique is the efficient conversion of an animated triangle mesh into a time-dependent implicit repre-
sentation based on closest surface points. The proposed technique is unconditionally stable with respect to the
surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on
the level of detail of the surface triangulation.

A Semi-Lagrangian Closest Point Method for Deforming Surfaces

Inyong Jeon, Kwang-Jin Choi, Tae-Yong Kim, Bong-Ouk Choi, and Hyeong-Seok Ko

We present a new technique which can handle both point and sliding constraints in the multigrid (MG) framework. Although the MG method can theoretically perform as fast as O(N), the development of a clothing simulator based on the MG method calls for solving an important technical challenge: handling the constraints. Resolving constrains has been difficult in MG because there has been no clear way to transfer the constraints existing in the finest level mesh to the coarser level meshes. This paper presents a new formulation based on soft constraints, which can coarsen the constraints defined in the finest level to the coarser levels. Experiments are performed which show that the proposed method can solve the linear system up to 4–9 times faster in comparison with the modified preconditioned conjugate gradient method (MPCG) without quality degradation. The proposed method is easy to implement and can be straightforwardly applied to existing clothing simulators which are based on implicit time integration.

Constrainable Multigrid for Cloth

N. Schmitt, Martin Knuth, Jan Bender, A. Kuijper

Today most cloth simulation systems use triangular mesh models. However, regular grids allow many optimizations as connectivity is implicit, warp and weft directions of the cloth are aligned to grid edges and distances between particles are equal. In this paper we introduce a cloth simulation that combines both model types. All operations that are performed on the CPU use a low-resolution triangle mesh while GPU-based methods are performed efficiently on a high-resolution grid representation. Both models are coupled by a sampling operation which renders triangle vertex data into a texture and by a corresponding projection of texel data onto a mesh. The presented scheme is very flexible and allows individual components to be performed on different architectures, data representations and detail levels. The results are combined using shader programs which causes a negligible overhead. We have implemented CPU-based collision handling and a GPU-based hierarchical constraint solver to simulate systems with more than 230k particles in real-time.

Multilevel Cloth Simulation using GPU Surface Sampling

Crispin Deul, Jan Bender

In this paper we present a novel multi-layer model for physically-based character skinning. In contrast to geometric approaches which are commonly used in the field of character skinning, physically-based methods can simulate secondary motion effects. Furthermore, these methods can handle collisions and preserve the volume of the model without the need of an additional post-process. Physically-based approaches are computationally more expensive than geometric methods but they provide more realistic results. Recent works in this area use finite element simulations to model the elastic behavior of skin. These methods require the generation of a volumetric mesh for the skin shape in a pre-processing step. It is not easy for an artist to model the different elastic behaviors of muscles, fat and skin using a volumetric mesh since there is no clear assignment between volume elements and tissue types. For our novel multi-layer model the mesh generation is very simple and can be performed automatically. Furthermore, the model contains a layer for each kind of tissue. Therefore, the artist can easily control the elastic behavior by adjusting the stiffness parameters for muscles, fat and skin. We use shape matching with oriented particles and a fast summation technique to simulate the elastic behavior of our skin model and a position-based constraint enforcement to handle collisions, volume conservation and the coupling of the skeleton with the deformable model. Position-based methods have the advantage that they are fast, unconditionally stable, controllable and provide visually plausible results.

Physically Based Character Skinning

Nadir Akinci, Gizem Akinci, Matthias Teschner

Realistic handling of fluid-air and fluid-solid interfaces in SPH is a challenging problem. The main reason is that some important physical phenomena such as surface tension and adhesion emerge as a result of inter-molecular forces in a microscopic scale. This is different from scalar fields such as fluid pressure, which can be plausibly evaluated on a macroscopic scale using particles. Although there exist techniques to address this problem for some specific simulation scenarios, there does not yet exist a general approach to reproduce the variety of effects that emerge in reality from fluid air and fluid-solid interactions. In order to address this problem, we present a new surface tension force and a new adhesion force. Different from the existing work, our surface tension force can handle large surface tensions in a realistic way. This property lets our approach handle challenging real scenarios, such as water crown formation, various types of fluid-solid interactions, and even droplet simulations. Furthermore, it prevents particle clustering at the free surface where inter-particle pressure forces are incorrect. Our adhesion force allows plausible two-way attraction of fluids and solids and can be used to model different wetting conditions. By using our forces, modeling surface tension and adhesion effects do not require involved techniques such as generating a ghost air phase or surface tracking. The forces are applied to the neighboring fluidfluid and fluid-boundary particle pairs in a symmetric way, which satisfies momentum conservation. We demonstrate that combining both forces allows simulating a variety of interesting effects in a plausible way.

Versatile Surface Tension and Adhesion for SPH Fluids