Month: July 2013

A New Grid Structure for Domain Extension

Bo Zhu, Wenlong Lu, Matthew Cong, Byungmoon Kim, Ronald Fedkiw

We present an efficient grid structure that extends a uniform grid to create a significantly larger far-field grid by dynamically extending the cells surrounding a fine uniform grid while still maintaining fine resolution about the regions of interest. The far-field grid preserves almost every computational advantage of uniform grids including cache coherency, regular subdivisions for parallelization, simple data layout, the existence of efficient numerical discretizations and algorithms for solving partial differential equations, etc. This allows fluid simulations to cover large domains that are often infeasible to enclose with sufficient resolution using a uniform grid, while still effectively capturing fine scale details in regions of interest using dynamic adaptivity.

A New Grid Structure for Domain Extension

A Level Set Method for Ductile Fracture

Jan Hegemann, Chenfanfu Jiang, Craig Schroeder, Joseph M. Teran

We utilize the shape derivative of the classical Griffith’s energy in a level set method for the simulation of dynamic ductile fracture. The level set is defined in the undeformed configuration of the object, and its evolution is designed to represent a transition from undamaged to failed material. No re-meshing is needed since the resulting topological changes are handled naturally by the level set method. We provide a new mechanism for the generation of fragments of material during the progression of the level set in the Griffith’s energy minimization. Collisions between different material pieces are resolved with impulses derived from the material point method over a background Eulerian grid. This provides a stable means for colliding with embedded interfaces. Simulation of corotational elasticity is based on an implicit finite element discretization.

A Level Set Method for Ductile Fracture

Efficient Simulation of Secondary Motion in Rig-Space

Fabian Hahn, Bernhard Thomaszewski, Stelian Coros, Sebastian Martin, Robert Sumner, Markus Gross

We present an efficient method for augmenting keyframed character animations with physically-simulated secondary motion. Our method achieves a performance improvement of one to two orders of magnitude over previous work without compromising on quality. This performance is based on a linearized formulation of rig-space dynamics that uses only rig parameters as degrees of freedom, a physics-based volumetric skinning method that allows our method to predict the motion of internal vertices solely from deformations of the surface, as well as a deferred Jacobian update scheme that drastically reduces the number of required rig evaluations. We demonstrate the performance of our method by comparing it to previous work and showcase its potential on a production-quality character rig.

Efficient Simulation of Secondary Motion in Rig-Space

Subspace Integration with Local Deformations

David Harmon, Denis Zorin

Subspace techniques greatly reduce the cost of nonlinear simulation by approximating deformations with a small custom basis. In order to represent the deformations well (in terms of a global metric), the basis functions usually have global support, and cannot capture localized deformations. While reduced-space basis functions can be localized to some extent, capturing truly local deformations would still require a very large number of precomputed basis functions, significantly degrading both precomputation and online performance. We present an efficient approach to handling local deformations that cannot be predicted, most commonly arising from contact and collisions, by augmenting the subspace basis with custom functions derived from analytic solutions to static loading problems. We also present a new cubature scheme designed to facilitate fast computation of the necessary runtime quantities while undergoing a changing basis. Our examples yield a two order of magnitude speedup over full-coordinate simulations, striking a desirable balance between runtime speeds and expressive ability.

Subspace Integration with Local Deformations

Thin Skin Elastodynamics

Duo Li, Shinjiro Sueda, Debanga R. Neog, Dinesh K. Pai

We present a novel approach to simulating thin hyperelastic skin. Real human skin is only a few millimeters thick. It can stretch and slide over underlying body structures such as muscles, bones, and tendons, revealing rich details of a moving character. Simulating such skin is challenging because it is in close contact with the body and shares its geometry. Despite major advances in simulating elastodynamics of cloth and soft bodies for computer graphics, such methods are difficult to use for simulating thin skin due to the need to deal with non-conforming meshes, collision detection, and contact response. We propose a novel Eulerian representation of skin that avoids all the difficulties of constraining the skin to lie on the body surface by working directly on the surface itself. Skin is modeled as a 2D hyperelastic membrane with arbitrary topology, which makes it easy to cover an entire character or object. Unlike most Eulerian simulations, we do not require a regular grid and can use triangular meshes to model body and skin geometry. The method is easy to implement, and can use low resolution meshes to animate high resolution details stored in texture-like maps. Skin movement is driven by the animation of body shape prescribed by an artist or by another simulation, and so it can be easily added as a post-processing stage to an existing animation pipeline. We provide several examples simulating human and animal skin, and skin-tight clothes.

Thin Skin Elastodynamics

A Hybrid Lagrangian-Eulerian Formulation for Bubble Generation and Dynamics

Saket Patkar, Mridul Aanjaneya, Dimitriy Karpman, Ronald Fedkiw

We present a hybrid Lagrangian-Eulerian framework for simulating both small and large scale bubble dynamics, where the bubbles can grow or shrink in volume as dictated by pressure forces in the surrounding fluid. Small under-resolved bubbles are evolved using Lagrangian particles that are monolithically two-way coupled to the surrounding flow in a manner that closely approximates the analytic bubble oscillation frequency while converging to the analytic volume as predicted by the well-known Rayleigh-Plesset equation. We present a novel scheme for interconverting between these under-resolved Lagrangian bubbles and larger well-resolved bubbles that are modeled with a traditional Eulerian level set approach. We also present a novel seeding mechanism to realistically generate bubbles when simulating fluid structure interaction with complex objects such as ship propellers. Moreover, our framework for bubble generation is general enough to be incorporated into all grid-based as well as particle-based fluid simulation methods.

A Hybrid Lagrangian-Eulerian Formulation for Bubble Generation and Dynamics