Month: September 2019

Yun (Raymond) Fei, Christopher Batty, Eitan Grinspun, Changxi Zheng

We propose a framework for simulating the complex dynamics of strands interacting with compressible, shear-dependent liquids, such as oil paint, mud, cream, melted chocolate, and pasta sauce. Our framework contains three main components: the strands modeled as discrete rods, the bulk liquid represented as a continuum (material point method), and a reduced-dimensional flow of liquid on the surface of the strands with detailed elastoviscoplastic behavior. These three components are tightly coupled together. To enable discrete strands interacting with continuum-based liquid, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. We also develop an extended constraint-based collision handling method that supports cohesion between strands. Furthermore, we present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We explore a series of challenging scenarios, involving splashing, shaking, and agitating the liquid which causes the strands to stick together and become entangled.

A Multi-Scale Model for Coupling Strands with Shear-Dependent Liquid

Zangyueyang Xian, Xin Tong, Tiantian Liu

We propose a simple yet efficient multigrid scheme to simulate high-resolution deformable objects in their full spaces at interactive frame rates. The point of departure of our method is the Galerkin projection which is simple to construct. However, a naive Galerkin multigrid does not scale well for large and irregular grids because it trades-off matrix sparsity for smaller sized linear systems which eventually stops improving the performance. Given that observation, we design our special projection criterion which is based on skinning space coordinates with piecewise constant weights, to make our Galerkin multigrid method scale for high-resolution meshes without suffering from dense linear solves. The usage of skinning space coordinates enables us to reduce the resolution of grids more aggressively, and our piecewise constant weights further ensure us to always deal with reasonably-sparse linear solves. Our projection matrices also help us to manage multi-level linear systems efficiently. Therefore, our method can be applied to different optimization schemes such as Newton’s method and Projective Dynamics, pushing the resolution of a real-time simulation to orders of magnitudes higher. Our final GPU implementation outperforms the other state-of-the-art GPU deformable body simulators, enabling us to simulate large deformable objects with hundred thousands of degrees of freedom in real-time.

A Scalable Galerkin Multigrid Method for Real-time Simulation of Deformable Objects