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

1° st Golden Rule: gaussian

Good analytics, but non-compact…

Gaussian

Linear/Ang Mom Conservation

Smooth and compact

Zero above r>2h C2-continuous: O(h^2) Insensitive to variance

Piecewise cubic

Super-Gaussian

W2=W4= … 0

Non-positive definite, Negative density near shocks

Variable Resolution

Discrete SParticles

Density

2°nd Golden Rule:Density inside

SPH Operators

p

q

Continuity

Momentum-Pressure

Momentum-Pressure

Show that:

Finally:

Viscosity

Viscosity

G-invariantZero for rigid bodiesLin-Ang Mom conserving

SPH Algorithm 1. Initial Conditions:

2. Density:

3. Gradients

4. Forces

SPH Algorithm 5. Move particles (MD-like)

“Potential”

Osmosis

Applications

entry Phil

Kernels