Large-scale liquid simulation on adaptive hexahedral grids

Florian Ferstl, Rudiger Westermann, Christian Dick

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


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.

Original languageEnglish
Article number6747389
Pages (from-to)1405-1417
Number of pages13
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number10
StatePublished - Oct 2014


  • Fluid simulation
  • finite elements
  • multigrid
  • octree


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