SIGGRAPH 2019

TOG:

A Geometrically Consistent Viscous Fluid Solver with Two-Way Fluid-Solid Coupling

Tetsuya Takahashi, Ming C. Lin.

We present a grid-based fluid solver for simulating viscous materials and their interactions with solid objects. Our method formulates the implicit viscosity integration as a minimization problem with consistently estimated volume fractions to account for the sub-grid details of free surfaces and solid boundaries. To handle the interplay between fluids and solid objects with viscosity forces, we also formulate the two-way fluid-solid coupling as a unified minimization problem based on the variational principle, which naturally enforces the boundary conditions. Our formulation leads to a symmetric positive definite linear system with a sparse matrix regardless of the monolithically coupled solid objects. Additionally, we present a position-correction method using density constraints to enforce the uniform distributions of fluid particles and thus prevent the loss of fluid volumes. We demonstrate the effectiveness of our method in a wide range of viscous fluid scenarios.

A Geometrically Consistent Viscous Fluid Solver with Two-Way Fluid-Solid Coupling

Efficient block pivoting for multibody simulations with contact

Andreas Enzenhoefer, Nicolas Lefebvre, Sheldon Andrews

Simulating stiff physical systems is a requirement for numerous computer graphics applications, such as VR training for heavy equipment operation. However, iterative linear solvers often perform poorly in such cases, and direct methods involving a factorization of the system matrix are typically preferred for accurate and stable simulations. This can have a detrimental impact on performance, since factorization of the system matrix is costly for complex simulations. In this paper, we present a method for efficiently solving linear systems of stiff physical systems involving contact, where the dynamics are modeled as a mixed linear complementarity problem (MLCP). Our approach is based on a block Bard-type algorithm that applies low-rank downdates to a Cholesky factorization of the system matrix at each pivoting step. Further performance improvements are realized by exploiting low bandwidth characteristics of the factorization. Our method gives up to 3.5 times speed-up versus recomputing the factorization based on the index set. Various challenging scenarios are used to demonstrate the advantages of our approach.

Efficient block pivoting for multibody simulations with contact

Aura Projection for Scalable Real-Time Physics

Alexander Brown, Gary Ushaw, Graham Morgan

In this paper we propose a solution to delivering scalable real-time physics simulations. Although high performance computing simulations of physics related problems do exist, these are not real-time and do not model the real-time intricate interactions of rigid bodies for visual effect common in video games (favouring accuracy over real-time). As such, this paper presents the first approach to real-time delivery of scalable, commercial grade, video game quality physics. This is achieved by taking the physics engine out of the player’s machine and deploying it across standard cloud based infrastructures. The simulation world is then divided into sections that are then allocated to servers. A server maintains the physics for all simulated objects in its section. Our contribution is the ability to maintain a scalable simulation by allowing object interaction across section boundaries using predictive migration techniques. We allow each object to project an aura that is used to determine object migration across servers to ensure seamless physics interactions between objects. The validity of our results is demonstrated through experimentation and benchmarking. Our approach allows player interaction at any point in real-time (influencing the simulation) in the same manner as any video game. We believe that this is the first successful demonstration of scalable real-time physics

Aura Projection for Scalable Real-Time Physics

Penalty Force for Coupling Materials with Coulomb Friction

Ounan Ding, Craig Schroeder

We propose a novel penalty force to enforce contacts with accurate Coulomb friction. The force is compatible with fully-implicit time integration and the use of optimization-based integration. The contact force is quite general. In addition to processing collisions between deformable objects, the force can be used to couple rigid bodies to deformable objects or the material point method.The force naturally leads to stable stacking without drift over time, even when solvers are not run to convergence. The force leads to an asymmetrical system, and we provide a practical solution for handling these.

Penalty Force for Coupling Materials with Coulomb Friction

Fast Quadrangular Mass-Spring Systems using Red-Black Ordering

Pontus Pall, Oskar Nylèn, Marco Fratarcangeli

We introduce a practical iterative solver for mass-spring systems which can be trivially mapped to massively parallel architectures, in particular GPUs.We employ our solver for the interactive animation of virtual cloth and show that it is computationally fast, robust and scalable, making it suitable for real-time graphics applications. Under the assumption that the input system is represented by a quadrangular network of masses connected by springs, we first partition the particles into two independent sets. Then, during the animation, the dynamics of all the particles belonging to each set is computed in parallel. This enables a full Gauss-Seidel iteration in just two parallel steps, leading to an approximated solution of large mass-spring systems in a few milliseconds. We use our solver to accelerate the solution of the popular Projective Dynamics framework, and compare it with other common iterative solvers in the current literature.

Fast Quadrangular Mass-Spring Systems using Red-Black Ordering

Laplacian Damping for Projective Dynamics

Jing Li, Tiantian Liu, Ladislav Kavan

Damping is an important ingredient in physics-based simulation of deformable objects. Recent work introduced new fast simulation methods such as Position Based Dynamics and Projective Dynamics. Explicit velocity damping methods currently used in conjunction with Position Based Dynamics or Projective Dynamics are simple and fast, but have some limitations. They may damp global motion or non-physically transport velocities throughout the simulated object. More advanced damping models do not have these limitations, but are slow to evaluate, defeating the benefits of fast solvers such as Projective Dynamics. We present a new type of damping model specifically designed for Projective Dynamics, which provides the quality of advanced damping models while adding only minimal computing overhead. The key idea is to define damping forces using Projective Dynamics’ Laplacian matrix. In a number of simulation examples we show that this damping model works very well in practice. When used with a modified Projective Dynamics solver that uses a non-dissipative implicit midpoint integrator, our damping method provides fully user-controllable damping, allowing the user to quickly produce visually pleasing and vivid animations.

Laplacian Damping for Projective Dynamics

Reformulating Hyperelastic Materials with Peridynamic Modeling

Liyou Xu, Xiaowei He, Wei Chen, Sheng Li, and Guoping Wang

Peridynamics is a formulation of the classical elastic theory that is targeted at simulating deformable objects with discontinuities, especially fractures. Till now, there are few studies that have been focused on how to model general hyperelastic materials with peridynamics. In this paper, we target at proposing a general strain energy function of hyperelastic materials for peridynamics. To get an intuitive model that can be easily controlled, we formulate the strain energy density function as a function parameterized by the dilatation and bond stretches, which can be decomposed into multiple one-dimensional functions independently. To account for nonlinear material behaviors, we also propose a set of nonlinear basis functions to help design a nonlinear strain energy function more easily. For an anisotropic material, we additionally introduce an anisotropic kernel to control the elastic behavior for each bond independently. Experiments show that our model is flexible enough to approximately regenerate various hyperelastic materials in classical elastic theory, including St.Venant-Kirchhoff and Neo-Hookean materi

Reformulating Hyperelastic Materials with Peridynamic Modeling

Accurate dissipative forces in optimization integrators

George E. Brown, Matthew Overby, Zahra Forootaninia, Rahul Narain

We propose a method for accurately simulating dissipative forces in deformable bodies when using optimization-based integrators. We represent such forces using dissipation functions which may be nonlinear in both positions and velocities, enabling us to model a range of dissipative effects including Coulomb friction, Rayleigh damping, and power-law dissipation. We propose a general method for incorporating dissipative forces into optimization-based time integration schemes, which hitherto have been applied almost exclusively to systems with only conservative forces. To improve accuracy and minimize artificial damping, we provide an optimization-based version of the second-order accurate TR-BDF2 integrator. Finally, we present a method for modifying arbitrary dissipation functions to conserve linear and angular momentum, allowing us to eliminate the artificial angular momentum loss caused by Rayleigh damping.

Accurate dissipative forces in optimization integrators

Interlinked SPH Pressure Solvers for Strong Fluid-Rigid Coupling

Christoph Gissler, Andreas Peer, Stefan Band, Jan Bender, Matthias Teschner

We present a strong fluid-rigid coupling for SPH fluids and rigid bodies with particle-sampled surfaces. The approach interlinks the iterative pressure update at fluid particles with a second SPH solver that computes artificial pressure at rigid body particles. The introduced SPH rigid body solver models rigid-rigid contacts as artificial density deviations at rigid body particles. The corresponding pressure is iteratively computed by solving a global formulation which is particularly useful for large numbers of rigid-rigid contacts. Compared to previous SPH coupling methods, the proposed concept stabilizes the fluid-rigid interface handling. It significantly reduces the computation times of SPH fluid simulations by enabling larger time steps. Performance gain factors of up to 58 compared to previous methods are presented. We illustrate the flexibility of the presented fluid-rigid coupling by integrating it into DFSPH, IISPH and a recent SPH solver for highly viscous fluids. We further show its applicability to a recent SPH solver for elastic objects. Large scenarios with up to 90M particles of various interacting materials and complex contact geometries with up to 90k rigid-rigid contacts are shown. We demonstrate the competitiveness of our proposed rigid body solver by comparing it to Bullet.

Interlinked SPH Pressure Solvers for Strong Fluid-Rigid Coupling