Technical Papers

Date/Time: 04 – 13 December 2020
All presentations are available in the virtual platform on-demand.

Lecturer(s):
David A. B. Hyde, University of California Los Angeles, United States of America
Steven W. Gagniere, University of California Los Angeles, United States of America
Alan Marquez-Razon, University of California Los Angeles, United States of America
Joseph Teran, University of California Los Angeles, United States of America

Bio:

Description: We present an updated Lagrangian discretization of surface tension forces for the simulation of liquids with moderate to extreme surface tension effects. The potential energy associated with surface tension is proportional to the surface area of the liquid. We design discrete forces as gradients of this energy with respect to the motion of the fluid over a time step. We show that this naturally allows for inversion of the Hessian of the potential energy required with the use of Newton’s method to solve the systems of nonlinear equations associated with implicit time stepping. The rotational invariance of the surface tension energy makes it non-convex and we define a definiteness fix procedure as in [Teran et al. 2005]. We design a novel level-set-based boundary quadrature technique to discretize the surface area calculation in our energy based formulation. Our approach works most naturally with Particle-In-Cell [Harlow 1964] techniques and we demonstrate our approach with a weakly incompressible model for liquid discretized with the Material Point Method [Sulsky et al. 1994]. We show that our approach is essential for allowing efficient implicit numerical integration in the limit of high surface tension materials like liquid metals.