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AC274: Smoothed Particle Hydrodynamics S. Succi

AC274: Smoothed Particle Hydrodynamics S. Succi. Large deformations: Grid-Free. Field: Overlap of smooth particles. Grid-free Dirac approximant. h: “ temperature ” =smooth. Moving Blobs:. FLUID: Overlap recommended!. General properties. Smoothing. Smoothing.

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AC274: Smoothed Particle Hydrodynamics S. Succi

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  1. AC274: Smoothed Particle Hydrodynamics S. Succi

  2. Large deformations: Grid-Free

  3. Field: Overlap of smooth particles

  4. Grid-free Dirac approximant h: “temperature”=smooth

  5. Moving Blobs: FLUID: Overlap recommended!

  6. General properties

  7. Smoothing

  8. Smoothing

  9. 1° st Golden Rule: gaussian Good analytics, but non-compact…

  10. Gaussian Linear/Ang Mom Conservation

  11. Smooth and compact Zero above r>2h C2-continuous: O(h^2) Insensitive to variance

  12. Piecewise cubic

  13. Super-Gaussian W2=W4= … 0 Non-positive definite, Negative density near shocks

  14. Variable Resolution

  15. Discrete SParticles

  16. Density

  17. 2°nd Golden Rule: Density inside

  18. SPH Operators q p

  19. Continuity

  20. Momentum-Pressure

  21. Momentum-Pressure Show that: Finally:

  22. Viscosity

  23. Viscosity G-invariant Zero for rigid bodies Lin-Ang Mom conserving

  24. SPH Algorithm • InitialConditions: 2. Density: 3. Gradients 4. Forces

  25. SPH Algorithm 5. Move particles (MD-like) “Potential”

  26. Osmosis

  27. Applications entry Phil

  28. Kernels

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