Month: September 2020

Rafael Nakanishi, Filipe Nascimento, Rafael Campos, Paulo Pagliosa, Afonso Paiva

We introduce a novel liquid simulation approach that combines a spatially adaptive pressure projection solver with the Particle-in-Cell (PIC) method. The solver relies on a generalized version of the Finite Difference (FD) method to approximate the pressure field and its gradients in tree-based grid discretizations, possibly non-graded. In our approach, FD stencils are computed by using meshfree interpolations provided by a variant of Radial Basis Function (RBF), known as RBF-Finite-Difference (RBF-FD). This meshfree version of the FD produces differentiation weights on scattered nodes with high-order accuracy. Our method adapts a quadtree/octree dynamically in a narrow-band around the liquid interface, providing an adaptive particle sampling for the PIC advection step. Furthermore, RBF affords an accurate scheme for velocity transfer between the grid and particles, keeping the system’s stability and avoiding numerical dissipation. We also present a data structure that connects the spatial subdivision of a quadtree/octree with the topology of its corresponding dual-graph. Our data structure makes the setup of stencils straightforward, allowing its updating without the need to rebuild it from scratch at each time-step. We show the effectiveness and accuracy of our solver by simulating incompressible inviscid fluids and comparing results with regular PIC-based solvers available in the literature.

RBF Liquids: An Adaptive Pic Solver Using RBF-FD

Tao Du, Kui Wu, Andrew Spielberg, Wojciech Matusik, Bo Zhu, Eftychios Sifakis

We present a method for performance-driven optimization of fluidic devices. In our approach, engineers provide a high-level specification of a device using parametric surfaces for the fluid-solid boundaries. They also specify desired flow properties for inlets and outlets of the device. Our computational approach optimizes the boundary of the fluidic device such that its steady-state flow matches desired flow at outlets. In order to deal with computational challenges of this task, we propose an efficient, differentiable Stokes flow solver. Our solver provides explicit access to gradients of performance metrics with respect to the parametric boundary representation. This key feature allows us to couple the solver with efficient gradient-based optimization methods. We demonstrate the efficacy of this approach on designs of five complex 3D fluidic systems. Our approach makes an important step towards practical computational design tools for high-performance fluidic devices.

Functional Optimization of Fluidic Devices with Differentiable Stokes Flow

Jiayi Eris Zhang, Seungbae Bang, David IW Levin, Alec Jacobson

We present a novel approach to enrich arbitrary rig animations with elastodynamic secondary effects. Unlike previous methods which pit rig displacements and physical forces as adversaries against each other, we advocate that physics should complement artists’ intentions. We propose optimizing for elastodynamic displacements in the subspace orthogonal to displacements that can be created by the rig. This ensures that the additional dynamic motions do not undo the rig animation. The complementary space is high dimensional, algebraically constructed without manual oversight, and capable of rich high-frequency dynamics. Unlike prior tracking methods, we do not require extra painted weights, segmentation into fixed and free regions or tracking clusters. Our method is agnostic to the physical model and plugs into non-linear FEM simulations, geometric as-rigid-as-possible energies, or mass-spring models. Our method does not require a particular type of rig and adds secondary effects to skeletal animations, cage-based deformations, wire deformers, motion capture data, and rigid-body simulations.

Complementary Dynamics

• 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