Physics-Based Animation

Chaoyang Lyu, Wei Li, Mathieu Desbrun, Xiaopei Liu

The intricate motions and complex vortical structures generated by the interaction between fluids and solids are visually fascinating. However, reproducing such a two-way coupling between thin objects and turbulent fluids numerically is notoriously challenging and computationally costly:
existing approaches such as cut-cell or immersed-boundary methods have
difficulty achieving physical accuracy, or even visual plausibility, of simulations involving fast-evolving flows with immersed objects of arbitrary shapes. In this paper, we propose an efficient and versatile approach for simulating two-way fluid-solid coupling within the kinetic (lattice-Boltzmann) fluid simulation framework, valid for both laminar and highly turbulent flows, and for both thick and thin objects. We introduce a novel hybrid approach to fluid-solid coupling which systematically involves a mesoscopic double-sided bounce-back scheme followed by a cut-cell velocity correction for a more robust and plausible treatment of turbulent flows near moving (thin) solids, preventing flow penetration and reducing boundary artifacts significantly. Coupled with an efficient approximation to simplify geometric computations, the whole boundary treatment method preserves the inherent massively parallel computational nature of the kinetic method. Moreover, we propose simple GPU optimizations of the core LBM algorithm which achieve an even higher computational efficiency than the state-of-the-art kinetic fluid solvers in graphics. We demonstrate the accuracy and efficacy of our two-way coupling through various challenging simulations involving a variety of rigid body solids and fluids at both high and low Reynolds numbers. Finally, comparisons to existing methods on benchmark data and real experiments further highlight the superiority of our method.

Fast and Versatile Fluid-Solid Coupling for Turbulent Flow Simulation

• Fast and Versatile Fluid-Solid Coupling for Turbulent Flow Simulation
• Predicting High-Resolution Turbulence Details in Space and Time
• Weatherscapes: Nowcasting Heat Transfer and Water Continuity
• Ships, Splashes, and Waves on a Vast Ocean
• A Material Point Method for Nonlinearly Magnetized Materials
• Interactive Cutting and Tearing in Projective Dynamics with Progressive Cholesky Updates
• I❤️LA: Compilable Markdown for Linear Algebra
• FrictionalMonolith: A Monolithic Optimization-based Approach for Granular Flow with Contact-Aware Rigid-Body Coupling
• Spiral-Spectral Fluid Simulation
• Generalized Fluid Carving With Fast Lattice-Guided Seam Computation
• PBNS: Physically Based Neural Simulation for Unsupervised Garment Pose Space Deformation

TOG:

• Locking-Proof Tetrahedra

Nghia Truong, Cem Yuksel, Chakrit Watcharopas, Joshua A. Levine, Robert M. Kirby

Robustly handling collisions between individual particles in a large particle-based simulation has been a challenging problem. We introduce particle merging-and-splitting, a simple scheme for robustly handling collisions between particles that prevents inter-penetrations of separate objects without introducing numerical instabilities. This scheme merges colliding particles at the beginning of the time-step and then splits them at the end of the time-step. Thus, collisions last for the duration of a time-step, allowing neighboring particles of the colliding particles to influence each other. We show that our merging-and-splitting method is effective in robustly handling collisions and avoiding penetrations in particle-based simulations. We also show how our merging-and-splitting approach can be used for coupling different simulation systems using different and otherwise incompatible integrators. We present simulation tests involving complex solid-fluid interactions, including solid fractures generated by fluid interactions.

Particle Merging-and-Splitting

Xu Wang, Makoto Fujisawa, Masahiko Mikawa

This paper introduces a method for simulating soil-structure coupling with water, which involves a series of visual effects, including wet granular materials, seepage flows, capillary action between grains, and dam breaking simulation. We develop a seepage flow based SPH-DEM framework to handle soil and water particles interactions through a momentum exchange term. In this framework, water is seen as a seepage flow through porous media by Darcy’s law; the seepage rate and the soil permeability are manipulated according to drag coefficient and soil porosity. A water saturation-based capillary model is used to capture various soil behaviors such as sandy soil and clay soil. Furthermore, the capillary model can dynamically adjust liquid bridge forces induced by surface tension between soil particles. The adhesion model describes the attraction ability between soil surfaces and water particles to achieve various visual effects for soil and water. Lastly, this framework can capture the complicated dam-breaking scenarios caused by overtopping flow or internal seepage erosion that are challenging to simulate.

Visual Simulation of Soil-Structure Destruction with Seepage Flows

Bruno Roy, Pierre Poulin, Eric Paquette

We present a novel up-resing technique for generating high-resolution liquids based on scene flow estimation using deep neural networks. Our approach infers and synthesizes small- and large-scale details solely from
a low-resolution particle-based liquid simulation. The proposed network
leverages neighborhood contributions to encode inherent liquid properties
throughout convolutions. We also propose a particle-based approach to interpolate between liquids generated from varying simulation discretizations using a state-of-the-art bidirectional optical flow solver method for fluids in addition with a novel key-event topological alignment constraint. In conjunction with the neighborhood contributions, our loss formulation allows the inference model throughout epochs to reward important differences in regard to significant gaps in simulation discretizations. Even when applied in an untested simulation setup, our approach is able to generate plausible high-resolution details. Using this interpolation approach and the predicted displacements, our approach combines the input liquid properties with the predicted motion to infer semi-Lagrangian advection. We furthermore show-case how the proposed interpolation approach can facilitate generating large simulation datasets with a subset of initial condition parameters.

Neural UpFlow: A Scene Flow Learning Approach to Increase the Apparent Resolution of Particle-Based Liquids

Seung Heon Sheen, Egor Larionov, Dinesh K. Pai

Simulation of human soft tissues in contact with their environment is essential in many fields, including visual effects and apparel design. Biological tissues are nearly incompressible. However, standard methods
employ compressible elasticity models and achieve incompressibility indirectly by setting Poisson’s ratio to be close to 0.5. This approach can produce results that are plausible qualitatively but inaccurate quantatively.
This approach also causes numerical instabilities and locking in coarse discretizations or otherwise poses a prohibitive restriction on the size of the time step. We propose a novel approach to alleviate these issues by replacing indirect volume preservation using Poisson’s ratios with direct enforcement of zonal volume constraints, while controlling fine-scale volumetric deformation through a cell-wise compression penalty.
To increase realism, we propose an epidermis model to mimic the dramatically higher surface stiffness on real skinned bodies. We demonstrate that our method produces stable realistic deformations with precise volume preservation but without locking artifacts. Due to the volume preservation not being tied to mesh discretization, our method also allows a resolution consistent simulation of incompressible materials. Our method improves the stability of the standard neo-Hookean model and the general compression recovery in the Stable neo-Hookean model.

Volume Preserving Simulation of Soft Tissue with Skin

Sheldon Andrews, Loic Nassif, Kenny Erleben, Paul Kry

We present a novel meso-scale model for computing anisotropic and asymmetric friction for contacts in rigid body simulations that is based on surface facet orientations. The main idea behind our approach is to compute a direction dependent friction coefficient that is determined by an object’s roughness. Specifically, where the friction is dependent on asperity interlocking, but at a scale where surface roughness is also a visual
characteristic of the surface. A GPU rendering pipeline is employed to rasterize surfaces using a shallow depth orthographic projection at each contact point in order to sample facet normal information from both surfaces, which we then combine to produce direction dependent friction coefficients that can be directly used in typical LCP contact solvers, such as the projected Gauss-Seidel method. We demonstrate our approach with a variety of rough textures, where the roughness is both visible in the rendering and in the motion produced by the physical simulation.

Coupling Friction with Visual Appearance

Tassilo Kugelstadt, Jan Bender, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Fabian Löschner and Andreas Longva

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [2018] originally devel-
oped for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with
SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the
implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a
state-of-the-art SPH simulator for elastic solids. We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

Tao Du, Kui Wu, Pingchuan Ma, Sebastien Wah, Andrew Spielberg, Daniela Rus, Wojciech Matusik

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using explicit time-stepping scheme require tiny time steps to avoid numerical instabilities in gradient computation, and simulators using implicit time integration typically compute gradients by employing the adjoint method and solving the expensive linearized dynamics. Inspired by Projective Dynamics (PD), we present Differentiable Projective Dynamics (DiffPD), an efficient differentiable soft-body simulator based on PD with implicit time integration. The key idea in DiffPD is to speed up backpropagation by exploiting the prefactorized Cholesky decomposition in forward PD simulation. In terms of contact handling, DiffPD supports two types of contacts: a penalty-based model describing contact and friction forces and a complementarity-based model enforcing non-penetration conditions and static friction. We evaluate the performance of DiffPD and observe it is 4-19 times faster compared to the standard Newton’s method in various applications including system identification, inverse design problems, trajectory optimization, and closed-loop control. We also apply DiffPD in a real-to-sim example with contact and collisions and show its capability of reconstructing a digital twin of real-world scenes.

DiffPD: Differentiable Projective Dynamics

Libo Huang, Ziyin Qu, Xun Tan, Xinxin Zhang, Dominik L. Michels, Chenfanfu Jiang

The simulation of large open water surface is challenging for a uniform volumetric discretization of the Navier-Stokes equation. The water splashes near moving objects, which height field methods for water waves cannot capture, necessitates high resolution simulation such as the Fluid-Implicit-Particle (FLIP) method. On the other hand, FLIP is not efficient for the long-lasting water waves that propagates to long distances, which requires sufficient depth for correct dispersion relationship. This paper presents a new method to tackle this dilemma through an efficient hybridization of volumetric and surface-based advection-projection discretizations. We design a hybrid time-stepping algorithm that combines a FLIP domain and an adaptively remeshed Boundary Element Method (BEM) domain for the incompressible Euler equations. The resulting framework captures the detailed water splashes near moving objects with FLIP, and produces convincing water waves with correct dispersion relationship at modest additional cost.

Ships, Splashes, and Waves on a Vast Ocean