A Versatile Energy‐Based SPH Surface Tension With Spatial Gradients

• Published in: Computer animation and virtual worlds Vol. 36; no. 3
• Main Authors: Wang, Qianwei, Xu, Yanrui, Sheng, Xiangyu, Yao, Chao, Guo, Yu, Chang, Jian, Zhang, Jianjun, Wang, Xiaokun
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.05.2025; Wiley Subscription Services, Inc
• Subjects: Energy; fluid simulation; interface energy; Interfaces; Kernel functions; Marangoni convection; Marangoni effect; Optimization; Smooth particle hydrodynamics; Surface tension; wetting
• ISSN: 1546-4261; 1546-427X
• DOI: 10.1002/cav.70057

ABSTRACT We propose a novel simulation method for surface tension effects based on the Smoothed Particle Hydrodynamics framework, capturing versatile tension effects using a unified interface energy description. Guided by the principle of energy minimization, we compute the interface energy from multiple interfaces solely using the original kernel function estimation, which eliminates the dependence on second‐order derivative discretization. Subsequently, we incorporate an inertia term into the energy function to strike a balance between tension effects and other forces. To simulate tension, we propose an energy diffusion‐based method for minimizing the objective energy function. The particles at the interface are iteratively shifted from high‐energy regions to low‐energy regions through several iterations, thereby achieving global interface energy minimization. Furthermore, our approach incorporates surface tension parameters as variable quantities within the energy framework, enabling automatic resolution of tension spatial gradients without requiring explicit computation of interfacial gradients. Experimental results demonstrate that our method effectively captures the wetting, capillary, and Marangoni effects, showcasing significant improvements in both the accuracy and stability of tension simulation. When a drop of soapy water is introduced into the center of the pool, the non‐uniform surface energy coefficient gives rise to a tension gradient. As a result, debris at the center of the pool is pulled outward by the tension–a phenomenon commonly known as the Marangoni effect.