Physics-Based Animation

Shiying Xiong, Rui Tao, Yaorui Zhang, Fan Feng, Bo Zhu

We propose a novel Lagrangian geometric representation using segment clouds to simulate incompressible fluid exhibiting strong anisotropic vortical features. The central component of our approach is a cloud of discrete segments enhanced by a set of local segment reseeding operations to facilitate both the geometrical evolution and the topological updates of vortical flow. We build a vortex dynamics solver with the support for dynamic solid boundaries based on discret segment primitives. We demonstrate the efficacy of our approach by simulating a broad range of challenging flow phenomena, such as reconnection of non-closed vortex tubes and vortex shedding behind a rotating object.

Incompressible flow simulation on vortex segment clouds

Shuqi Yang, Shiying Xiong, Yaorui Zhang, Fan Feng, Jinyuan Liu, Bo Zhu

We propose a novel gauge fluid solver based on Clebsch wave functions to solve incompressible fluid equations. Our method combines the expressive power of Clebsch wave functions to represent coherent vortical structures and the generality of gauge methods to accommodate a broad array of fluid phenomena. By evolving a transformed wave function as the system’s gauge variable enhanced by an additional projection step to enforce pressure jumps on the free boundaries, our method can significantly improve the vorticity generation and preservation ability for a broad range of gaseous and liquid phenomena. Our approach can be easily implemented by modifying a standard grid-based fluid simulator. It can be used to solve various fluid dynamics, including complex vortex filament dynamics, fluids with different obstacles, and surface-tension flow.

Clebsch Gauge Fluid

Rene Winchenbach, Andreas Kolb

In this paper we propose an improved refinement process for the simulation of incompressible low-viscosity turbulent flows using Smoothed Particle Hydrodynamics, under adaptive volume ratios of up to 1 : 1,000,000. We derive a discretized objective function, which allows us to generate ideal refinement patterns for any kernel function and any number of particles a priori without requiring intuitive initial user-input. We also demonstrate how this objective function can be optimized online to further improve the refinement process during simulations by utilizing a gradient descent and a modified evolutionary optimization. Our investigation reveals an inherent residual refinement error term, which we smooth out using improved and novel methods. Our improved adaptive method is able to simulate adaptive volume ratios of1 : 1,000,000and higher, even under highly turbulent flows,only being limited by memory consumption. In general, we achieve more than an order of magnitude greater adaptive volume ratios than prior work.

Optimized Refinement for Spatially Adaptive SPH

Kai Jia

Solving nonlinear systems is an important problem. Numerical continuation methods efficiently solve certain nonlinear systems. The Asymptotic Numerical Method (ANM) is a powerful continuation method that usually converges faster than Newtonian methods. ANM explores the landscape of the function by following a parameterized solution curve approximated with a high-order power series. Although ANM has successfully solved a few graphics and engineering problems, prior to our work, applying ANM to new problems required significant effort because the standard ANM assumes quadratic functions, while manually deriving the power series expansion for nonquadratic systems is a tedious and challenging task. This paper presents a novel solver, SANM, that applies ANM to solve symbolically represented nonlinear systems. SANM solves such systems in a fully automated manner. SANM also extends ANM to support many nonquadratic operators, including intricate ones such as singular value decomposition. Furthermore, SANM generalizes ANM to support the implicit homotopy form. Moreover, SANM achieves high computing performance via optimized system design and implementation. We deploy SANM to solve forward and inverse elastic force equilibrium problems and controlled mesh deformation problems with a few constitutive models. Our results show that SANM converges faster than Newtonian solvers, requires little programming effort for new problems, and delivers comparable or better performance than a hand-coded, specialized ANM solver. While we demonstrate on mesh deformation problems, SANM is generic and potentially applicable to many tasks.

SANM: A Symbolic Asymptotic Numerical Solver with Applications in Mesh Deformation

Mengdi Wang, Yitong Deng, Xiangxin Kong, Aditya H. Prasad, Shiying Xiong, Bo Zhu

We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton’s interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

Thin-Film Smoothed Particle Hydrodynamics Fluid

Liangwang Ruan, Jinyuan Liu, Bo Zhu, Shinjiro Sueda, Bin Wang, Baoquan Chen

We propose a novel three-way coupling method to model the contact interaction between solid and fluid driven by strong surface tension. At the heart of our physical model is a thin liquid membrane that simultaneously couples to both the liquid volume and the rigid objects, facilitating accurate momentum transfer, collision processing, and surface tension calculation. This model is implemented numerically under a hybrid Eulerian-Lagrangian framework where the membrane is modelled as a simplicial mesh and the liquid volume is simulated on a background Cartesian grid. We devise a monolithic solver to solve the interactions among the three systems of liquid, solid, and membrane. We demonstrate the efficacy of our method through an array of rigid-fluid contact simulations dominated by strong surface tension, which enables the faithful modeling of a host of new surface-tension-dominant phenomena including: objects with higher density than water can keep afloat on top of it; ‘Cheerios effect’ about floating objects that do not normally float attract one another; surface tension weakening effect caused by surface-active constituents.

Solid-Fluid Interaction with Surface-Tension-Dominant Contact

Jingyu Chen, Victoria Kala, Ala Marquez-Razon, Elias Gueidon, David A. B. Hyde, Joseph Teran

We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration. Furthermore, since the surface energy is an interfacial property depending on the types of materials on either side of an interface, spatial variation is required for modeling the contact angle at the triple junction between a liquid, solid and surrounding air. Our discretization is based onthe surface energy itself, rather than on the associated traction condition most commonly used for discretization with particle methods. Our energy based approach automatically captures surface gradients without the explicit need to resolve them as in traction condition based approaches. We include an implicit discretization of thermomechanical material coupling with anovel particle-based enforcement of Robin boundary conditions associated with convective heating. Lastly, we design a particle resampling approach needed to achieve perfect conservation of linear and angular momentum with Affine-Particle-In-Cell (APIC) [Jiang et al.2015]. We show that our approach enables implicit time stepping for complex behaviors like the Marangoni effect and hydrophobicity/hydrophilicity. We demonstrate the robustness and utility of our method by simulating materials that exhibit highly diverse degrees of surface tension and thermomechanical effects,such as water, wine and wax.

A Momentum-Conserving Implicit Material Point Method for Surface Tension with Contact Angles and Spatial Gradients

Jiong Chen, Florian Schäfer, Jin Huang, Mathieu Desbrun

Many computer graphics applications boil down to solving sparse systems of linear equations. While the current arsenal of numerical solvers available in various specialized libraries and for different computer architectures often allow efficient and scalable solutions to image processing, modeling and simulation applications, an increasing number of graphics problems face large-scale and ill-conditioned sparse linear systems — a numerical challenge which typically chokes both direct factorizations (due to high memory requirements) and iterative solvers (because of slow convergence). We propose a novel approach to the efficient preconditioning of such problems which often emerge from the discretization over unstructured meshes of partial differential equations with heterogeneous and anisotropic coefficients. Our numerical approach consists in simply performing a fine-to-coarse ordering and a multiscale sparsity pattern of the degrees of freedom, using which we apply an incomplete Cholesky factorization. By further leveraging supernodes for cache coherence, graph coloring to improve parallelism and partial diagonal shifting to remedy negative pivots, we obtain a preconditioner which, combined with a conjugate gradient solver, far exceeds the performance of existing carefully-engineered libraries for graphics problems involving bad mesh elements and/or high contrast of coefficients. We also back the core concepts behind our simple solver with theoretical foundations linking the recent method of operator-adapted wavelets used in numerical homogenization to the traditional Cholesky factorization of a matrix, providing us with a clear bridge between incomplete Cholesky factorization and multiscale analysis that we leverage numerically.

Multiscale Cholesky Preconditioning for Ill-conditioned Problems

Siyuan Shen, Yang Yin, Tianjia Shao, He Wang, Chenfanfu Jiang, Lei Lan, Kun Zhou

This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable solids. Due to the inertia effect, the dynamic equilibrium cannot be established without evaluating the second-order derivatives of the deep autoencoder network. This is beyond the capability of off-the-shelf automatic differentiation packages and algorithms, which mainly focus on the gradient evaluation. Solving the nonlinear force equilibrium is even more challenging if the standard Newton’s method is to be used. This is because we need to compute a third-order derivative of the network to obtain the variational Hessian. We attack those difficulties by exploiting complex-step finite difference, coupled with reverse automatic differentiation. This strategy allows us to enjoy the convenience and accuracy of complex-step finite difference and in the meantime, to deploy complex-value perturbations as collectively as possible to save excessive network passes.With a GPU-based implementation, we are able to wield deep autoencoders(e.g.,10+layers) with a relatively high-dimension latent space in real-time.Along this pipeline, we also design a sampling network and a weighting net-work to enable weight-varying Cubature integration in order to incorporate nonlinearity in the model reduction. We believe this work will inspire and benefit future research efforts in nonlinearly reduced physical simulation problems.

High-order Differentiable Autoencoder for Nonlinear Model Reduction

Huamin Wang

In this paper, we study physics-based cloth simulation in a very high reso-lution setting, presumably at submillimeter levels with millions of vertices,to meet perceptual precision of our human eyes. State-of-the-art simulation techniques, mostly developed for unstructured triangular meshes, can hardly meet this demand due to their large computational costs and memory footprints. We argue that in a very high resolution, it is more plausible touse regular meshes with an underlying grid structure, which can be highly compatible with GPU acceleration like high-resolution images. Based on this idea, we formulate and solve the nonlinear optimization problem for simulating high-resolution wrinkles, by a fast block-based descent method with reduced memory accesses. We also investigate the development of the collision handling component in our system, whose performance benefits greatly from the grid structure. Finally, we explore various issues related tothe applications of our system, including initialization for fast convergence and temporal coherence, gathering effects, inflation and stuffing models,and mesh simplification. We can treat our system as a quasistatic wrinkle synthesis tool, run it as a standalone dynamic simulator, or integrate it into a multi-resolution solver as an additional component. The experiment demonstrates the capability, efficiency and flexibility of our system in producing avariety of high-resolution wrinkles effects.

GPU-Based Simulation of Cloth Wrinkles at Submillimeter Levels