Physics-Based Animation

• Monolith: A Monolithic Pressure-Viscosity-Contact Solver for Strong Two-Way Rigid-Rigid Rigid-Fluid Coupling
• A Novel Discretization and Numerical Solver for Non-Fourier Diffusion
• Complementary Dynamics
• Functional Optimization of Fluid Devices with Differentiable Stokes Flow
• Surface-Only Ferrofluids
• RBF Liquids: An Adaptive PIC Solve Using RBF-FD
• Simulation, Modeling and Authoring of Glaciers
• Stormscapes: Simulating Cloud Dynamics in the Now
• P-Cloth: Interactive Complex Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators
• An Extended Cut-cell method for Sub-Grid Liquids Tracking with Surface Tension
• An Adaptive Staggered-Tilted Grid for Incompressible Flow Simulation
• ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact
• A Moving Least Square Reproducing Kernel Particle Method for Unified Multiphase Continuum Simulation
• Interactive Liquid Splash Modeling by User Sketches
• Frequency-Domain Smoke Guiding
• Semi-Analytic Boundary Handling Below Particle Resolution for Smoothed Particle Hydrodynamics
• An Implicit Updated Lagrangian Formulation for Liquids with Large Surface Energy
• Higher-Order Finite Elements for Embedded Simulation
• Learning to Manipulate Amorphous Materials
• A Harmonic Balance Approach for Designing Compliant Mechanical Systems with Nonlinear Periodic Motions

Tao Xue, Haozhe Su, Chengguizi Han, Chenfanfu Jiang, Mridul Aanjaneya

We introduce the C-F diffusion model [Anderson and Tamma 2006; Xue et al.2018] to computer graphics for diffusion-driven problems that has several attractive properties: (a) it fundamentally explains diffusion from the perspective of the non-equilibrium statistical mechanical Boltzmann TransportE quation, (b) it allows for a finite propagation speed for diffusion, in contrast to the widely employed Fick’s/Fourier’s law, and (c) it can capture some of the most characteristic visual aspects of diffusion-driven physics, such as hydrogel swelling, limited diffusive domain for smoke flow, snowflake and dendrite formation, that span from Fourier-type to non-Fourier-type diffusive phenomena. We propose a unified convection-diffusion formulationusing this model that treats both the diffusive quantity and its associated flux as the primary unknowns, and that recovers the traditional Fourier-type diffusion as a limiting case. We design a novel semi-implicit discretization for this formulation on staggered MAC grids and a geometric Multigrid-preconditioned Conjugate Gradients solver for efficient numerical solution.To highlight the efficacy of our method, we demonstrate end-to-end examples of elastic porous media simulated with the Material Point Method (MPM), and diffusion-driven Eulerian incompressible fluids.

A Novel Discretization and Numerical Solver for Non-Fourier Diffusion

Yu Fang*, Ziyin Qu*, Minchen Li, Xinxin Zhang, Yixin Zhu, Mridul Aanjaneya, Chenfanfu Jiang

We propose a novel scheme for simulating two-way coupled interactions between nonlinear elastic solids and incompressible fluids. The key ingredient of this approach is a ghost matrix operator-splitting scheme for strongly coupled nonlinear elastica and incompressible fluids through the weak form of their governing equations. This leads to a stable and efficient method handling large time steps under the CFL limit while using a single monolithic solve for the coupled pressure fields, even in the case with highly nonlinear elastic solids. The use of the Material Point Method (MPM) is essential in the designing of the scheme, it not only preserves discretization consistency with the hybrid Lagrangian-Eulerian fluid solver, but also works naturally with our novel interface quadrature (IQ) discretization for free-slip boundary conditions. While traditional MPM suffers from sticky numerical artifacts, our framework naturally supports discontinuous tangential velocities at the solid-fluid interface. Our IQ discretization results in an easy-to-implement, fully particle-based treatment of the interfacial boundary, avoiding the additional complexities associated with intermediate level set or explicit mesh representations. The efficacy of the proposed scheme is verified by various challenging simulations with fluid-elastica interactions.

IQ-MPM: An Interface Quadrature Material Point Method for Non-sticky Strongly Two-Way Coupled Nonlinear Solids and Fluids

Doug L. James

Physics-based simulations of deforming tetrahedral meshes are widely used to animate detailed embedded geometry. Unfortunately most practitioners still use linear interpolation (or other low-order schemes) on tetrahedra, which can produce undesirable visual artifacts, e.g., faceting and shading artifacts, that necessitate increasing the simulation’s spatial resolution and, unfortunately, cost. In this paper, we propose Phong Deformation, a simple, robust and practical vertex-based quadratic interpolation scheme that, while still only C0 continuous like linear interpolation, greatly reduces visual artifacts for embedded geometry. The method first averages element-based linear deformation models to vertices, then barycentrically interpolates the vertex models while also averaging with the traditional linear interpolation model. The method is a fast, robust, and easily implemented replacement for linear interpolation that produces visually better results for embedded deformation with irregular tetrahedral meshes.

Phong Deformation: A better C0 interpolant for embedded deformation

Joshuah Wolper, Yunuo Chen, Minchen Li, Yu Fang, Ziyin Qu, Jiecong Lu, Meggie Cheng, Chenfanfu Jiang

Dynamic fracture surrounds us in our day-to-day lives, but animating this phenomenon is notoriously difficult and only further complicated by anisotropic materials—those with underlying structures that dictate preferred fracture directions. Thus, we present AnisoMPM: a robust and general approach for animating the dynamic fracture of isotropic, transversely isotropic, and orthotropic materials. AnisoMPM has three core components: a technique for anisotropic damage evolution, methods for anisotropic elastic response, and a coupling approach. For anisotropic damage, we adopt a non-local continuum damage mechanics (CDM) geometric approach to crack modeling and augment this with structural tensors to encode material anisotropy. Furthermore, we discretize our damage evolution with explicit and implicit integration, giving a high degree of computational efficiency and flexibility. We also utilize a QR-decomposition based anisotropic constitutive model that is inversion safe, more efficient than SVD models, easy to implement, robust to extreme deformations, and that captures all aforementioned modes of anisotropy. Our elasto-damage coupling is enforced through an additive decomposition of our hyperelasticity into a tensile and compressive component in which damage is used to degrade the tensile contribution to allow for material separation. For extremely stiff fibered materials, we further introduce a novel Galerkin weak form discretization that enables embedded directional inextensibility. We present this as a hard-constrained grid velocity solve that poses an alternative to our anisotropic elasticity that is locking-free and can model very stiff materials.

AnisoMPM: Animating Anisotropic Damage Mechanics

Jan Bender, Tassilo Kugelstadt, Marcel Weiler, Dan Koschier

In this paper, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. Firstly, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

Implicit Frictional Boundary Handling for SPH

Xingyu Ni, Bo Zhu, Bin Wang, Baoquan Chen

We present a versatile numerical approach to simulating various magnetic phenomena using a level-set method. At the heart of our method lies a novel two-way coupling mechanism between a magnetic field and a magnetizable mechanical system, which is based on the interfacial Helmholtz force drawn from the Minkowski form of the Maxwell stress tensor. We show that a magnetic-mechanical coupling system can be solved as an interfacial problem, both theoretically and computationally. In particular, we employ a Poisson equation with a jump condition across the interface to model the mechanical-to-magnetic interaction and a Helmholtz force on the free surface to model the magnetic-to-mechanical effects. Our computational framework can be easily integrated into a standard Euler fluid solver, enabling both simulation and visualization of a complex magnetic field and its interaction with immersed magnetizable objects in a large domain. We demonstrate the efficacy of our method through an array of magnetic substance simulations that exhibit rich geometric and dynamic characteristics, encompassing ferrofluid, rigid magnetic body, deformable magnetic body, and multi-phase couplings.

A Level-Set Method for Magnetic Substance Simulation

Hui Wang, Yongxu Jin, Anqi Luo, Xubo Yang, Bo Zhu

We propose a new Eulerian-Lagrangian approach to simulate the various surface tension phenomena characterized by volume, thin sheets, thin filaments, and points using Moving-Least-Squares (MLS) particles. At the center of our approach is a meshless Lagrangian description of the different types of codimensional geometries and their transitions using an MLS approximation. In particular, we differentiate the codimension-1 and codimension-2 geometries on Lagrangian MLS particles to precisely describe the evolution of thin sheets and filaments, and we discretize the codimension-0 operators on a background Cartesian grid for efficient volumetric processing. Physical forces including surface tension and pressure across different codimensions are coupled in a monolithic manner by solving one single linear system to evolve the surface-tension driven Navier-Stokes system in a complex non-manifold space. The codimensional transitions are handled explicitly by tracking a codimension number stored on each particle, which replaces the tedious meshing operators in a conventional mesh-based approach. Using the proposed framework, we simulate a broad array of visually appealing surface tension phenomena, including the fluid chain, bell, polygon, catenoid, and dripping, to demonstrate the efficacy of our approach in capturing the complex fluid characteristics with mixed codimensions, in a robust, versatile, and connectivity-free manner.

Codimensional Surface Tension Flow using Moving-Least-Squares Particles

Christoph Gissler, Andreas Henne, Stefan Band, Andreas Peer, Matthias Teschner

Snow is a complex material. It resists elastic normal and shear deformations, while some deformations are plastic. Snow can deform and break. It can be significantly compressed and gets harder under compression. Existingsnow solvers produce impressive results. E.g., hybrid Lagrangian/Euleriantechniques have been used to capture all material properties of snow. The auxiliary grid, however, makes it challenging to handle small volumes. In particular, snow fall and accumulation on surfaces have not been demonstrated with these solvers yet. Existing particle-based snow solvers, on the other hand, can naturally handle small snow volumes. However, existing solutions consider simplified material properties. In particular, shear deformation and the hardening effect are typically omitted. We present a novel Lagrangian snow approach based on Smoothed Particle Hydrodynamics (SPH). Snow is modeled as an elastoplastic continuous material that captures all above-mentioned effects. The compression of snow is handled by a novel compressible pressure solver, where the typically employed state equation is replaced by an implicit formulation. Acceleration due to shear stress is computed using a second implicit formulation. The linear solvers of the two implicit formulations for accelerations due to shear and normal stress are realized with matrix-free implementations. Using implicit formulations and solving them with matrix-free solvers al-lows to couple the snow to other phases and is beneficial to the stability and the time step size, i.e., performance of the approach. Solid boundaries are represented with particles and a novel implicit formulation is used to handle friction at solid boundaries. We show that our approach can simulate accumulation, deformation, breaking, compression and hardening of snow. Furthermore, we demonstrate two-way coupling with rigid bodies, interaction with incompressible and highly viscous fluids and phase change from fluid to snow.

An Implicit Compressible SPH Solver for Snow Simulation

Tomas Skrivan, Andreas Soderstrom, John Johansson, Christoph Sprenger, Ken Museth, Chris Wojtan

We propose a method to enhance the visual detail of a water surface simula-tion. Our method works as a post-processing step which takes a simulationas input and increases its apparent resolution by simulating many detailedLagrangian water waves on top of it. We extend linear water wave theoryto work in non-planar domains which deform over time, and we discretizethe theory using Lagrangian wave packets attached to spline curves. Themethod is numerically stable and trivially parallelizable, and it produceshigh frequency ripples with dispersive wave-like behaviors customized tothe underlying fluid simulation.

Wave Curves: Simulating Lagrangian water waves on dynamically deforming surfaces