Functional fluids on surfaces

Omri Azencot, Steffen Weißmann, Maks Ovsjanikov, Max Wardetzky, Mirela Ben-Chen

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an incompressible fluid on a curved surface represented as an unstructured triangle mesh. Unlike the commonly used Eulerian description of the fluid using its time-varying velocity field, we propose to model fluids using their vorticity, i.e., by a (time varying) scalar function on the surface. During each time step, we advance scalar vorticity along two consecutive, stationary velocity fields. This approach leads to a variational integrator in the space continuous setting. In addition, using this approach, the update rule amounts to manipulating functions on the surface using linear operators, which can be discretized efficiently using the recently introduced functional approach to vector fields. Combining these time and space discretizations leads to a conceptually and algorithmically simple approach, which is efficient, time-reversible and conserves vorticity by construction. We further demonstrate that our method exhibits no numerical dissipation and is able to reproduce intricate phenomena such as vortex shedding from boundaries.

Original languageEnglish GB
Pages (from-to)237-246
Number of pages10
JournalComputer Graphics Forum
Volume33
Issue number5
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

Keywords

  • Categories and Subject Descriptors (according to ACM CCS)
  • Computer Graphics [I.3.5]: Computational Geometry and Object Modeling - Physically based modeling
  • Computer Graphics [I.3.7]: Three-Dimensional Graphics and Realism - Animation

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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