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Smoothed Particle Hydrodynamics Techniques for the Physics Based - - PowerPoint PPT Presentation
Smoothed Particle Hydrodynamics Techniques for the Physics Based - - PowerPoint PPT Presentation
Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids Rigid Bodies Dan Jan Barbara Matthias Koschier Bender Solenthaler Teschner Graphics Research - SPH Solver Fluids Low viscosity
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SPH Rigid-Body Solver
Sample surfaces with particles Map contact to artificial density deviation Compute pressure Pressure accelerations resolve contacts Pressure system differs from fluids as accelerations are applied to entire rigid bodies (sets of particles) instead
- f single particles
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[Gissler et al., presented at ACM SIGGRAPH 2019]
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Formulation
Rigid-body surface particles with artificial rest density, e.g. Contact: Continuity equation: Time discretization at : Constraint :
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Concept
Find velocities for rigid-body particles such that Map unknown velocities to unknown artificial pressure per particle Pressure corresponds to a pressure / contact force Forces change linear / angular momentum of the entire rigid body such that all particles have the desired velocities
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Illustration
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One equation per particle with unknown particle velocity One equation per particle with unknown body velocities
Reformulating the System
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One equation per particle with unknown contact forces One equation per particle with unknown pressures
Reformulating the System
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Solver
SPH discretization of
Two loops over all rigid particles Standard SPH forms for
Jacobi iterations
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Strong Fluid-Rigid Coupling
Iterative rigid-body solver Iterative fluid solver, e.g. PCISPH, IISPH, DFSPH Interleaved fluid-rigid velocity update Rigid solver iteration updates predicted velocities of rigid particles Fluid solver iteration updates predicted velocities of fluid particles
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[Gissler et al., presented at ACM SIGGRAPH 2019]
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[Gissler et al., presented at ACM SIGGRAPH 2019]
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[Gissler et al., presented at ACM SIGGRAPH 2019]
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