Mathematical Foundation of the Optimization-based Fluid Animation Method

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dc.contributor.authorErleben, Kennyen_US
dc.contributor.authorMisztal, Marek Krzysztofen_US
dc.contributor.authorBæren, J. Andreasen_US
dc.contributor.editorA. Bargteil and M. van de Panneen_US
dc.date.accessioned2013-10-31T10:28:34Z
dc.date.available2013-10-31T10:28:34Z
dc.date.issued2011en_US
dc.description.abstractWe present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to be able to handle advection in a numerically simple Lagrangian approach. Following this a finite element method is used for the remaining terms of the fractional step method. The key to deriving a discretization for the diffusion forces lies inrestating the momentum equations in terms of a Newtonian stress tensor. Rather than applying a straightforward temporal finite difference method followed by a projection method to enforce incompressibility as done in the stable fluids method, the last step of the fractional step method is rewritten as an optimization problem to make it easy to incorporate non-linear force terms such as surface tension.en_US
dc.description.seriesinformationEurographics/ ACM SIGGRAPH Symposium on Computer Animationen_US
dc.identifier.isbn978-1-4503-0923-3en_US
dc.identifier.issn1727-5288en_US
dc.identifier.urihttps://doi.org/10.2312/SCA/SCA11/101-110en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectComputational Fluid Dynamics, Unstructured Meshes, Finite Element Method, Optimizationbased Fluid Animation, Diffusion Forces, Deformable Simplicial Complexes. Categories and Subject Descriptors (according to ACM CCS): Computer Graphics [I.3.5]: Physically based modeling-Computer Graphics [I.3.7]: Animation-Mathematics of Computing [G.1.6]: Nonlinearprogrammingen_US
dc.titleMathematical Foundation of the Optimization-based Fluid Animation Methoden_US
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SCA 11: Eurographics/SIGGRAPH Symposium on Computer Animation