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A PML Based Non-Reflective Boundary for Free Surface Fluid Animation
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Applied Thermodynamics and Fluid Mechanics . Linköping University, The Institute of Technology.
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology. (Dreamworks Animation)
2010 (English)In: ACM Transactions on Graphics, ISSN 0730-0301, E-ISSN 1557-7368, Vol. 29, no 5, 136- p.Article in journal (Refereed) Published
Abstract [en]

This article presents a novel non-reflective boundary condition for the free surface incompressible Euler and Navier-Stokes equations. Boundaries of this type are very useful when, for example, simulating water flow around a ship moving over a wide ocean. Normally waves generated by the ship will reflect off of the boundaries of the simulation domain and as these reflected waves returns towards the ship they will cause undesired interference patterns.By employing a Perfectly Matched Layer (PML) approach we have derived a boundary condition that absorbs incoming waves and thus efficiently prevents these undesired wave reflections. To solve the resulting boundary equations we present a fast and stable algorithm based on the Stable Fluids approach. Through numerical experiments we then show that our boundaries are significantly more effective than simpler reflection preventing techniques. We also provide a thorough analysis of the parameters involved in our boundary formulation and show how they effect wave absorption efficiency.

Place, publisher, year, edition, pages
New York, NY, USA: ACM , 2010. Vol. 29, no 5, 136- p.
Keyword [en]
Computational fluid dynamics, Free surface, Stable Fluids, Euler equations, Navier-Stokes equations, Non-reflecting boundary condition, Perfectly matched layer
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-60850DOI: 10.1145/1857907.1857912ISI: 000284285600005OAI: diva2:359547
Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2010-12-14
In thesis
1. Memory Efficient Methods for Eulerian Free Surface Fluid Animation
Open this publication in new window or tab >>Memory Efficient Methods for Eulerian Free Surface Fluid Animation
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis focuses on improving and extending the available toolset for Eulerian, i.e. grid based, free surface fluid animation and level set based surface tracking in the context of computer graphics and visual effects. More specifically three novel methods are presented each aimed towards reducing the amount of computer memory required for producing high resolution animations of incompressible free surface fluids. Each method is primarily developed for, but not limited to, the popular Stable Fluids method.

Eulerian free surface fluid animation has historically required a large amount of computer memory, especially when high resolution results are desired. This problem has recently been addressed through the development of dynamic computational grids like the Dynamic Tubular Grid (DT-Grid) for level set computations. However, when animating free surface fluids a large amount of tracker particles are often added to the level set geometry in order to provide more accurate tracking of fluid surfaces. As a result the particle level set (PLS) method typically requires two orders of magnitude more memory than a DT-Grid level set. In order to reduce the gap in memory requirement between the level set and the particles this thesis introduces a fast and efficient compression method for such tracker particles. This compression is optionally combined with a specialized external memory algorithm that allows particle and level set data to be efficiently streamed back and forth between primary memory and secondary storage devices such as hard disk drives. The particle compression scheme is able to reduce the size of a DT-Grid particle level set by more than 65% while only inducing a 5% penalty to performance. If combined with the external memory algorithm particle level sets of virtually any size and resolution can be used in free surface fluid animations. The induced performance penalty of the combined scheme depends on the performance of the external storage device, however when using a traditional hard disk drive a 70% increase in simulation time was measured.

This thesis also presents a purely Eulerian alternative to the PLS method through the introduction of a dual resolution level set representation. The method replaces the tracker particles with a level set of higher resolution, thus significantly increasing surface tracking accuracy compared to the unaided level set. The scheme is able to produce high quality results using up to 94% less memory than a PLS. The core component of the method is the Spatially Adaptive Morphology (SAM) filter which connects the high resolution representation of the level set with the lower resolution fluid, thus providing plausable animation also for small and/or thin surface features. A sheet preserving extension to the SAM filter is also presented that is able to preserve thin sheets of fluid indefinitely if so desired. Although this method adds mass to the simulation it is highly useful for animating phenomena like splashes, fountains and waterfalls.

The final method presented in this thesis concerns the efficient local animation of oceans and other very large free surface fluids.For such scenarios large amounts of memory and computation time can be saved by only computing accurate fluid physics in a local fluid region immediately surrounding a point of interest. The fluid outside this region can then be animated using less accurate but significantly faster and less memory demanding models. However, for this approach to be accurate the local fluid must be contained in such a way that it behaves as if still part of a larger fluid. This thesis enables the local simulation of a larger body of fluid by introducing three different non-reflective boundary conditions for free surface fluid animation using a modified Stable Fluids method. Two simple wave dampening boundaries are presented as well as a significantly more advanced wave absorbing boundary based on the Perfectly Matched Layer (PML) approach. All three boundaries are shown to be effective in preventing wave reflection given large enough boundary regions. However the PML boundary is significantly more efficient, typically absorbing waves at a fraction of the distance required by the other two methods.

Place, publisher, year, edition, pages
Linköping: Linköping Universisty Electronic Press, 2010. 138 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1345
National Category
Engineering and Technology
urn:nbn:se:liu:diva-60852 (URN)978-91-7393-295-0 (ISBN)
Public defence
2010-12-03, K3, Kåkenhus, Campus Norrköping, Linköpings Universitet, Norrköping, 09:30 (English)
Available from: 2010-11-16 Created: 2010-10-28 Last updated: 2010-11-16Bibliographically approved

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Söderström, AndreasKarlsson, MattsMuseth, Ken
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