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Issue No.03 - March (2012 vol.18)
pp: 516-526
K. Bodin , Umed Univ., Umea, Sweden
C. Lacoursiere , Umed Univ., Umea, Sweden
M. Servin , Dept. of Phys., Umed Univ., Umea, Sweden
ABSTRACT
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.
INDEX TERMS
iterative methods, computational fluid dynamics, computer graphics, digital simulation, hydrodynamics, interactive simulations, constraint fluids, fluid simulation method, smoothed particle hydrodynamics, incompressibility conditions, boundary conditions, holonomic kinematic constraints, systematic multiphysics integration, fluid pseudoparticles, Archimedes principle, buoyancy, SPOOK, mixed linear complementarity problem, fast iterative method, computer graphics applications, Force, Equations, Mathematical model, Computer graphics, Approximation methods, Computational modeling, Stability analysis, variational integrator., SPH, incompressible, constraints, fluid simulation
CITATION
K. Bodin, C. Lacoursiere, M. Servin, "Constraint Fluids", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 3, pp. 516-526, March 2012, doi:10.1109/TVCG.2011.29
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