A Cut-Cell Geometric Multigrid Poisson Solver for Fluid Simulation

• Published in: Computer graphics forum Vol. 34; no. 2; pp. 481 - 491
• Main Authors: Weber, Daniel, Mueller-Roemer, Johannes, Stork, André, Fellner, Dieter
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.05.2015
• Subjects: Analysis; Categories and Subject Descriptors (according to ACM CCS); Computational fluid dynamics; Computer graphics; Convergence; Fluid flow; Fluids; Formulations; Hierarchies; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Physically based modeling; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism -Animation; Image processing systems; Mathematical analysis; Simulation; Solvers; Studies
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12577

We present a novel multigrid scheme based on a cut‐cell formulation on regular staggered grids which generates compatible systems of linear equations on all levels of the multigrid hierarchy. This geometrically motivated formulation is derived from a finite volume approach and exhibits an improved rate of convergence compared to previous methods. Existing fluid solvers with voxelized domains can directly benefit from this approach by only modifying the representation of the non‐fluid domain. The necessary building blocks are fully parallelizable and can therefore benefit from multi‐ and many‐core architectures.