Shusen Liu, Yuzhong Guo, Lixin Ren, Ying Qiao, Xiaowei He
Simulating free-surface flows requires capturing the effects of incompress-
ibility, viscosity, and surface tension. Existing particle-based methods often
rely on operator splitting, which introduces coupling artifacts and limits sta-
bility. We propose a unified nonlinear optimization framework that achieves
a strong coupling of these three effects within a single solver. By leveraging
peridynamics, we formulate the discretization of distinct fluid mechanisms
under a consistent variational principle. Specifically, we recast fluid mo-
tion as a nonlinear variational optimization problem over particle positions,
which is solved via the semi-implicit successive substitution method. More-
over, the framework incorporates separate treatments for bulk and shear
viscosity, allowing for more refined control of different viscous fluid behav-
iors. To the best of our knowledge, this is the first particle-based unified
solver capable of fully resolving the interdependence of incompressibility,
viscosity, and surface tension, thereby significantly enhancing stability in
complex simulations of free-surface flows. The source code for the paper is
publicly available at https://github.com/peridyno/peridyno.
A Nonlocal Monolithic Variational Framework for Free Surface Flows