Hongyi Xu, Yili Zhao, and Jernej Barbic
The penalty method is a simple and popular approach to resolving contact in computer graphics and robotics. Penalty-based contact, however, suffers from stability problems due to the highly variable and unpredictable net stiffness, and this is particularly pronounced in simulations with time-varying distributed geometrically complex contact. We employ semi-implicit integration, exact analytical contact gradients, symbolic Gaussian elimination and a SVD solver to simulate stable penalty-based frictional contact with large, time-varying contact
areas, involving many rigid objects and articulated rigid objects in complex conforming contact and self-contact. We also derive implicit proportional-derivative control forces for real-time control of articulated structures with loops. We present challenging contact scenarios such as screwing a hexbolt into a hole, bowls stacked in perfectly conforming configurations, and manipulating many objects using actively controlled articulated mechanisms in real time.
Implicit Multibody Penalty-based Distributed Contact
Robin Tomcin, Dominik Sibbing, Leif Kobbelt
In rigid body simulation, one must distinguish between contacts (so-called unilateral constraints) and articulations (bilateral constraints). For contacts and friction, iterative solution methods have proven most useful for interactive applications, often in combination with Shock-Propagation in cases with strong interactions between contacts (such as stacks), prioritizing performance and plausibility over accuracy. For articulation constraints, direct solution methods are preferred, because one can rely on a factorization with linear time complexity for tree-like systems, even in ill-conditioned cases caused by large mass-ratios or high complexity. Despite recent advances, combining the advantages of direct and iterative solution methods wrt. performance has proven difficult and the intricacy of articulations in interactive applications is often limited by the convergence speed of the iterative solution method in the presence of closed kinematic loops (i.e. auxiliary constraints) and contacts. We identify common performance bottlenecks in the dynamic simulation of unilateral and bilateral constraints and are able to present a simulation method, that scales well in the number of constraints even in ill-conditioned cases with frictional contacts, collisions and closed loops in the kinematic graph. For cases where many joints are connected to a single body, we propose a technique to increase the sparsity of the positive definite linear system. A solution to these bottlenecks is presented in this paper to make the simulation of a wider range of mechanisms possible in real-time without extensive parameter tuning.
Efficient Enforcement of Hard Articulation Constraints in the Presence of Closed Loops and Contacts
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