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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 Boundary Handling Dan Jan Barbara Matthias Koschier Bender Solenthaler Teschner SPH Fluid Solver Neighbor search Incompressibility
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Outline
Particle boundaries Current developments
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Concept
Boundaries are sampled with particles that contribute to density, pressure and pressure acceleration of the fluid Boundary handling: How to compute ?
Fluid particle Solid particles Kernel support
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Several Layers with Uniform Boundary Samples
Boundary particles are handled as static fluid samples Pressure acceleration
Fluid Solid
Contributions from fluid neighbors Contributions from boundary neighbors Boundary neighbors contribute to the density All samples have the same size, i.e. same mass and rest density All samples have the same size, i.e. same mass and rest density
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Pressure at Boundary Samples
Pressure acceleration at boundaries requires pressure at boundary samples Various solutions, e.g. mirroring, extrapolation, PPE Mirroring
Formulation with unknown boundary pressure Mirroring of pressure and density from fluid to boundary
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Boundary Contribution to Pressure Acceleration
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One Layer of Uniform Boundary Samples
Contributions of missing samples have to be added Pressure acceleration
Fluid Solid
Offset typically implemen- ted as scaling coefficient
Missing samples
x is an approximation
- f the contribution from
missing samples Kernel property Kernel gradient property Pseudo inverse
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Correction of Missing Contributions
The motivation of and is to compensate contributions of missing samples to
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One Layer of Non-Uniform Boundary Samples
Non-uniform contributions from boundary samples Pressure acceleration
Fluid Solid
Contribution, i.e. mass
- f a boundary sample is
approximated from its boundary neighbors
Missing samples
Non-uniform sizes, i.e. masses of boundary samples
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One Layer of Non-Uniform Boundary Samples
In 3D,
For perfect sampling For perfect sampling For arbitrary sampling
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Typical Boundary Representation
Color-coded volume
- f boundary samples
Boundary samples
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Rigid-Fluid Coupling
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Rigid-Fluid Coupling
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Summary
Boundary is sampled with static fluid particles One layer of non-uniform samples
Arbitrary triangulated meshes can be used as boundary Non-uniform boundary samples can be handled Missing contributions to fluid density and pressure acceleration have to be corrected Pressure is mirrored from fluid to boundary
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Outline
Particle boundaries Current developments
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Current Developments
Pressure extrapolation [Adami 2012, Band 2018] Solving boundary pressure with a PPE [Band 2018] Density maps [Koschier 2017]
Precomputing boundary contributions to the density computation of nearby fluid particles
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