Implicit Formulation for SPH-Based Viscous Fluids

Tetsuya Takahashi, Yoshinori Dobashi, Issei Fujishiro, Tomoyuki Nishita, Ming C. Lin

We propose a stable and efficient particle-based method for simulating highly viscous fluids that can generate coiling and buckling phenomena and handle variable viscosity. In contrast to previous methods that use explicit integration, our method uses an implicit formulation to improve the robustness of viscosity integration, therefore enabling use of larger time steps and higher viscosities. We use Smoothed Particle Hydrodynamics to solve the full form of viscosity, constructing a sparse linear system with a symmetric positive definite matrix, while exploiting the variational principle that automatically enforces the boundary condition on free surfaces. We also propose a new method for extracting coefficients of the matrix contributed by second-ring neighbor particles to efficiently solve the linear system using a conjugate gradient solver. Several examples demonstrate the robustness and efficiency of our implicit formulation over previous methods and illustrate the versatility of our method.

Implicit Formulation for SPH-Based Viscous Fluids

Eurographics 2015

Physics-based animation papers at Eurographics 2015:

A Dimension-reduced Pressure Solver for Liquid Simulations

Ryoichi Ando, Nils Thuerey, Chris Wojtan

This work presents a method for efficiently simplifying the pressure projection step in a liquid simulation. We first devise a straightforward dimension reduction technique that dramatically reduces the cost of solving the pressure projection. Next, we introduce a novel change of basis that satisfies free-surface boundary conditions {\em exactly}, regardless of the accuracy of the pressure solve. When combined, these ideas greatly reduce the computational complexity of the pressure solve without compromising free surface boundary conditions at the highest level of detail. Our techniques are easy to parallelize, and they effectively eliminate the computational bottleneck for large liquid simulations.

A Dimension-reduced Pressure Solver for Liquid Simulations

 

Yarn-Level Simulation of Woven Cloth

Gabriel Cirio, Jorge Lopez-Moreno, David Miraut, Miguel A. Otaduy

The large-scale mechanical behavior of woven cloth is determined by the mechanical properties of the yarns, the weave pattern, and frictional contact between yarns. Using standard simulation methods for elastic rod models and yarn-yarn contact handling, the simulation of woven garments at realistic yarn densities is deemed intractable. This paper introduces an efficient solution for simulating woven cloth at the yarn level. Central to our solution is a novel discretization of interlaced yarns based on yarn crossings and yarn sliding, which allows modeling yarn-yarn contact implicitly, avoiding contact handling at yarn crossings altogether. Combined with models for internal yarn forces and inter-yarn frictional contact, as well as a massively parallel solver, we are able to simulate garments with hundreds of thousands of yarn crossings at practical framerates on a desktop machine, showing combinations of large-scale and fine-scale effects induced by yarn-level mechanics.

Yarn-Level Simulation of Woven Cloth

Interactive Material Design Using Model Reduction

Hongyi Xu, Yijing Li, Yong Chen, Jernej Barbic

We demonstrate an interactive method to create heterogeneous continuous deformable materials on complex three-dimensional meshes. The user specifies displacements and internal elastic forces at a chosen set of mesh vertices. Our system then rapidly solves an optimization problem to compute a corresponding heterogeneous spatial distribution of material properties, using the Finite Element Method (FEM) analysis. We apply our method to linear and nonlinear isotropic deformable materials. We demonstrate that solving the problem interactively in the full-dimensional space of individual tetrahedron material values is not practical. Instead, we propose a new model reduction method that projects the material space to a low dimensional space of material modes. Our model reduction accelerates optimization by two orders of magnitude, and makes the convergence much
more robust, making it possible to interactively design material distributions on complex meshes.We apply our method to precise control of contact forces and control of pressure over large contact areas between rigid and deformable objects for ergonomics. Our tetrahedron-based dithering method can efficiently convert continuous material distributions into discrete ones and we demonstrate its precision via FEM simulation. We physically display our distributions using haptics, as well as demonstrate how haptics can aid in the material design. The produced heterogeneous material distributions can also be used in computer animation applications.

Interactive Material Design Using Model Reduction

Realistic Biomechanical Simulation and Control of Human Swimming

Weiguang Si, Sung-Hee Lee, Eftychios Sifakis, Demetri Terzopoulos

We address the challenging problem of controlling a complex biomechanical model of the human body to synthesize realistic swimming animation. Our human model includes all of the relevant articular bones and muscles, including 103 bones (comprising 163 articular degrees of freedom) plus a total of 823 muscle actuators embedded in a finite element model of the musculotendinous soft tissues of the body that produces realistic deformations. To coordinate the numerous muscle actuators in order to produce natural swimming movements, we develop a biomimetically motivated motor control system based on Central Pattern Generators (CPG), which learns to produce activation signals that drive the numerous muscle actuators.

Realistic Biomechanical Simulation and Control of Human Swimming

Strain Limiting for Clustered Shape Matching

Adam W. Bargteil, Ben Jones

In this paper, we advocate explicit symplectic Euler integration and strain limiting in a shape matching simulation framework. The resulting approach resembles not only previous work on shape matching and strain limiting, but also the recently popular position-based dynamics.However, unlike this previous work, our approach reduces to explicit integration under small strains, but remains stable in the presence of non-linearities.

Strain Limiting for Clustered Shape Matching

Multi-layer skin simulation with adaptive constraints

Pengbo Li, Paul Kry

We present an approach for physics based simulation of the wrinkling of multi-layer skin with heterogeneous material properties. Each layer of skin is simulated with an adaptive mesh, with the different layers coupled via constraints that only permit wrinkle deformation at wavelengths that match the physical properties of the multi-layer model. We use texture maps to define varying elasticity and thickness of the skin layers, and design our constraints as continuous functions, which we discretize at run time to match the changing adaptive mesh topology. In our examples, we use blend shapes to drive the bottom layer, and we present a variety of examples of simulations that demonstrate small wrinkles on top of larger wrinkles, which is a typical pattern seen on human skin. Finally, we show that our physics-based wrinkles can be used in the automatic creation of wrinkle maps, allowing the visual details of our high resolution simulations to be produced at real time speeds.

Multi-layer skin simulation with adaptive constraints

Windy Trees: Computing Stress Response for Developmental Tree Models

Sören Pirk, Till Niese, Torsten Hädrich, Bedrich Benes, Oliver Deussen

We present a novel method for combining developmental tree models with turbulent wind fields. The tree geometry is created from internal growth functions of the developmental model and its response to external stress is induced by a physically-plausible wind field that is simulated by Smoothed Particle Hydrodynamics (SPH). Our tree models are dynamically evolving complex systems that (1) react in real-time to high-frequent changes of the wind simulation; and (2) adapt to long-term wind stress. We extend this process by wind-related effects such as branch breaking as well as bud abrasion and drying. In our interactive system the user can adjust the parameters of the growth model, modify wind properties and resulting forces, and define the tree’s long-term response to wind. By using graphics hardware, our implementation runs at interactive rates for moderately large scenes composed of up to 20 tree models.

Windy Trees: Computing Stress Response for Developmental Tree Models

SPGrid: A Sparse Paged Grid structure applied to adaptive smoke simulation

Rajsekhar Setaluri, Mridul Aanjaneya, Sean Bauer, and Eftychios Sifakis

We introduce a new method for fluid simulation on high-resolution adaptive grids which rivals the throughput and parallelism potential of methods based on uniform grids. Our enabling contribution is SPGrid, a new data structure for compact storage and efficient stream processing of sparsely populated uniform Cartesian grids.SPGrid leverages the extensive hardware acceleration mechanisms inherent in the x86 Virtual Memory Management system to deliver sequential and stencil access bandwidth comparable to dense uniform grids. Second, we eschew tree-based adaptive data structures in favor of storing simulation variables in a pyramid of sparsely populated uniform grids, thus avoiding the cost of indirect memory access associated with pointer-based representations. We show how the costliest algorithmic kernels of fluid simulation can be implemented as a composition of two kernel types: (a) stencil operations on a single sparse uniform grid, and (b) structured data transfers between adjacent levels of resolution, even when modeling non-graded octrees. Finally, we demonstrate an adaptive multigridpreconditioned Conjugate Gradient solver that achieves resolutionindependent convergence rates while admitting a lightweight implementation with a modest memory footprint. Our method is complemented by a new interpolation scheme that reduces dissipative effects and simplifies dynamic grid adaptation. We demonstrate the efficacy of our method in end-to-end simulations of smoke flow.

SPGrid: A Sparse Paged Grid structure applied to adaptive smoke simulation