Markus Ihmsen, Jens Orthmann, Barbara Solenthaler, Andreas Kolb, and Matthias Teschner
Smoothed Particle Hydrodynamics (SPH) has been established as one of the major concepts for fluid animation in computer graphics. While SPH initially gained popularity for interactive free-surface scenarios, it has emerged to be a fully fledged technique for state-of-the-art fluid animation with versatile effects. Nowadays, complex scenes with millions of sampling points, one- and two-way coupled rigid and elastic solids, multiple phases and additional features such as foam or air bubbles can be computed at reasonable expense. This state-of-the-art report summarizes SPH research within the graphics community.
SPH Fluids in Computer Graphics
B. Jones, S. Ward, A. Jallepalli, J. Perenia, and A. W. Bargteil
We present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space, the least-squares best fit of the material’s rest state into three dimensions. Nearest neighbor queries in the embedded space efficiently update particle neighborhoods to account for plastic flow. These queries are simpler and more efficient than remeshing strategies employed in mesh-based finite element methods. We also introduce a new estimate for the volume of a particle, allowing particle masses to vary spatially and temporally with fixed density. Our approach can handle simultaneous extreme elastic and plastic deformations. We demonstrate our approach on a variety of examples that exhibit a wide range of material behaviors.
Deformation Embedding for Point-Based Elastoplastic Simulation
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