Tetrahedral Embedded Boundary Methods for Accurate and Flexible Adaptive Fluids

When simulating fluids, tetrahedral methods provide flexibility and ease of adaptivity that Cartesian grids find difficult to match. However, this approach has so far been limited by two conflicting requirements. First, accurate simulation requires quality Delaunay meshes and the use of circumcentri...

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Bibliographic Details
Published in:Computer graphics forum Vol. 29; no. 2; pp. 695 - 704
Main Authors: Batty, Christopher, Xenos, Stefan, Houston, Ben
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.05.2010
Subjects:
Alignment
Boundaries
Computational fluid dynamics
Computer simulation
Finite element method
Flexibility
Fluid flow
Fluids
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Physically based modeling
I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Animation
Image processing systems
Simulation
Velocity
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:When simulating fluids, tetrahedral methods provide flexibility and ease of adaptivity that Cartesian grids find difficult to match. However, this approach has so far been limited by two conflicting requirements. First, accurate simulation requires quality Delaunay meshes and the use of circumcentric pressures. Second, meshes must align with potentially complex moving surfaces and boundaries, necessitating continuous remeshing. Unfortunately, sacrificing mesh quality in favour of speed yields inaccurate velocities and simulation artifacts. We describe how to eliminate the boundary‐matching constraint by adapting recent embedded boundary techniques to tetrahedra, so that neither air nor solid boundaries need to align with mesh geometry. This enables the use of high quality, arbitrarily graded, non‐conforming Delaunay meshes, which are simpler and faster to generate. Temporal coherence can also be exploited by reusing meshes over adjacent timesteps to further reduce meshing costs. Lastly, our free surface boundary condition eliminates the spurious currents that previous methods exhibited for slow or static scenarios. We provide several examples demonstrating that our efficient tetrahedral embedded boundary method can substantially increase the flexibility and accuracy of adaptive Eulerian fluid simulation.
Bibliography:ark:/67375/WNG-SCPGPTWN-M
istex:5D46530C2D69B8DC6BB224353A9F1BEE8D53C5CA
ArticleID:CGF1639
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01639.x