Conference paper
Mathematical foundation of the optimization-based fluid animation method
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.
Language: | English |
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Publisher: | ACM |
Year: | 2011 |
Pages: | 101-110 |
Proceedings: | 34th International Conference and Exhibition on Computer Graphics and Interactive Techniques |
ISBN: | 1450309232 and 9781450309233 |
Types: | Conference paper |
DOI: | 10.1145/2019406.2019420 |
ORCIDs: | 0000-0001-6808-4747 and Bærentzen, Jakob Andreas |
Computational Fluid Dynamics Deformable Simplicial Complexes Diffusion Forces Finite Element Method Optimizationbased Fluid Animation Unstructured Meshes
Animation Computer graphics Computing methodologies Continuous mathematics Design and analysis of algorithms Geometric topology Mathematical analysis Mathematical optimization Mathematics of computing Physical simulation Shape modeling Theory of computation Topology computational fluid dynamics computational fluid dynamics, deformable simplicial complexes, diffusion forces, finite element method, optimization-based fluid animation, unstructured meshes deformable simplicial complexes diffusion forces finite element method optimization-based fluid animation unstructured meshes