Incompressible SPH using the Divergence-Free Condition

• Published in: Computer graphics forum Vol. 33; no. 7; pp. 219 - 228
• Main Authors: Kang, Nahyup, Sagong, Donghoon
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.10.2014
• Subjects: Analysis; Categories and Subject Descriptors (according to ACM CCS); Computer graphics; Computer simulation; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Physically based modeling; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Animation; Studies
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12490

In this paper, we present a novel SPH framework to simulate incompressible fluid that satisfies both the divergence‐ free condition and the density‐invariant condition. In our framework, the two conditions are applied separately. First, the divergence‐free condition is enforced when solving the momentum equation. Later, the density‐invariant condition is applied after the time integration of the particle positions. Our framework is a purely Lagrangian approach so that no auxiliary grid is required. Compared to the previous density‐invariant based SPH methods, the proposed method is more accurate due to the explicit satisfaction of the divergence‐free condition. We also propose a modified boundary particle method for handling the free‐slip condition. In addition, two simple but effective methods are proposed to reduce the particle clumping artifact induced by the density‐invariant condition.