Constraint Fluids

• Published in: IEEE transactions on visualization and computer graphics Vol. 18; no. 3; pp. 516 - 526
• Main Authors: Bodin, K., Lacoursiere, C., Servin, M.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01-03-2012; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation methods; Boundary conditions; Computational fluid dynamics; Computational modeling; Computer Graphics; Computer Simulation; constraints; Density; Equations; Fluid flow; fluid simulation; Fluids; Force; Hydrodynamics; incompressible; Mathematical model; Mathematical models; Models, Theoretical; SPH; Stability analysis; Studies; variational integrator
• ISSN: 1077-2626; 1941-0506; 1941-0506
• DOI: 10.1109/TVCG.2011.29

We present a fluid simulation method based on Smoothed Particle Hydrodynamics (SPH) in which incompressibility and boundary conditions are enforced using holonomic kinematic constraints on the density. This formulation enables systematic multiphysics integration in which interactions are modeled via similar constraints between the fluid pseudoparticles and impenetrable surfaces of other bodies. These conditions embody Archimede's principle for solids and thus buoyancy results as a direct consequence. We use a variational time stepping scheme suitable for general constrained multibody systems we call SPOOK. Each step requires the solution of only one Mixed Linear Complementarity Problem (MLCP) with very few inequalities, corresponding to solid boundary conditions. We solve this MLCP with a fast iterative method. Overall stability is vastly improved in comparison to the unconstrained version of SPH, and this allows much larger time steps, and an increase in overall performance by two orders of magnitude. Proof of concept is given for computer graphics applications and interactive simulations.