Mathematical foundation of the optimization-based fluid animation method

Kenny Erleben, Marek Krzysztof Misztal, Jakob Andreas Bærentzen

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    Abstract

    We 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 in restating 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.
    Original languageEnglish
    Title of host publicationSCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
    EditorsA. Bargteil, M. van de Panne
    Number of pages10
    PublisherACM
    Publication date2011
    Pages101-110
    ISBN (Print)978-1-4503-0923-3
    DOIs
    Publication statusPublished - 2011
    Event34th International Conference and Exhibition on Computer Graphics and Interactive Techniques - San Diego, CA, United States
    Duration: 5 Aug 20079 Aug 2007
    Conference number: 34
    http://www.siggraph.org/s2007/

    Conference

    Conference34th International Conference and Exhibition on Computer Graphics and Interactive Techniques
    Number34
    CountryUnited States
    CitySan Diego, CA
    Period05/08/200709/08/2007
    Internet address

    Keywords

    • Optimizationbased Fluid Animation
    • Unstructured Meshes
    • Finite Element Method
    • Deformable Simplicial Complexes
    • Diffusion Forces
    • Computational Fluid Dynamics

    Cite this

    Erleben, K., Misztal, M. K., & Bærentzen, J. A. (2011). Mathematical foundation of the optimization-based fluid animation method. In A. Bargteil, & M. van de Panne (Eds.), SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (pp. 101-110). ACM. https://doi.org/10.1145/2019406.2019420