Functional Fluids on Surfaces

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 triang...

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Veröffentlicht in:Computer graphics forum Jg. 33; H. 5; S. 237 - 246
Hauptverfasser: Azencot, Omri, Weißmann, Steffen, Ovsjanikov, Maks, Wardetzky, Max, Ben-Chen, Mirela
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Blackwell Publishing Ltd 01.08.2014
Schlagworte:
Algorithms
Analysis
Categories and Subject Descriptors (according to ACM CCS)
Computational fluid dynamics
Computer graphics
Computer Graphics [I.3.5]: Computational Geometry and Object Modeling-Physically based modeling
Computer Graphics [I.3.7]: Three-Dimensional Graphics and Realism-Animation
Computer simulation
Fluid flow
Fluids
Mathematical analysis
Mathematical models
Scalars
Simulation
Studies
Vorticity
ISSN:0167-7055, 1467-8659
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:istex:0838F1D1938B938EC7D8144EF8163F12AB9AD196
ark:/67375/WNG-95PMN4BC-L
Supporting Information
ArticleID:CGF12449
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12449