Fakultät Informatik

Octree Fluid Simulation using Finite Elements

 Florian Ferstl, Rüdiger Westermann and  Christian Dick

Department of Computer Science, Technische Universität München, Germany



Regular grids are attractive for numerical fluid simulations because they give rise to efficient computational kernels. However, for simulating high resolution effects in complicated domains they are only of limited suitability due to memory constraints. In this paper we present a method for liquid simulation on  an adaptive octree grid using a hexahedral finite element discretization, which reduces memory requirements by coarsening the elements in the interior of the liquid body. To impose free surface boundary conditions with second order accuracy, we incorporate a particular class of Nitsche methods enforcing the Dirichlet boundary conditions for the pressure in a variational sense. We then show how to construct a multigrid hierarchy from the adaptive octree grid, so that a time efficient geometric multigrid solver can be used. To improve solver convergence, we propose a special treatment of liquid boundaries via composite finite elements at coarser scales. We demonstrate the effectiveness of our method for liquid simulations that would require hundreds of millions of simulation elements in a non-adaptive regime.

Associated publications

Large-Scale Liquid Simulation on Adaptive Hexahedral Grids
Florian Ferstl, Rüdiger Westermann and Christian Dick,
IEEE Transactions on Visualization and Computer Graphics, accepted for publication [PDF][BIBTEX]

Presented at SCA2014 [SLIDES].

Submission Video



Matthias Niessner, our new Professor from Stanford University, offers a number of interesting topics for  master theses.


PhD positions on   Computational Fabrication and 3D Printing and  Photorealistic Rendering for Deep Learning and Online Reconstruction are available at the Computer Graphics & Visualization group.