Erleben, KennyMisztal, Marek KrzysztofBæren, J. AndreasA. Bargteil and M. van de Panne2013-10-312013-10-312011978-1-4503-0923-31727-5288https://doi.org/10.2312/SCA/SCA11/101-110We 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.Computational 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]: Nonlinearprogramming