A compressible fluid particle model based on the Voronoi ...
A compressible fluid particle model based on the Voronoi ...
A compressible fluid particle model based on the Voronoi ...
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Vor<strong>on</strong>oi<br />
Final Reversible<br />
equati<strong>on</strong>s<br />
dRi () t = Vi<br />
dt<br />
,<br />
dmi = 0<br />
dt<br />
,<br />
dSi<br />
= 0<br />
dt<br />
dV<br />
⎛ c i<br />
ij e ⎞ ij<br />
m i = ∑ Aij⎜<br />
− ⎟(<br />
Pi − Pj)<br />
dt ⎜<br />
j≠i Rij<br />
2 ⎟<br />
⎝ ⎠<br />
The analogy is a quantitative relati<strong>on</strong>ship, because <strong>on</strong>e can dem<strong>on</strong>strate<br />
1 ∂v<br />
1 ⎛ ⎞<br />
j<br />
cij eij<br />
∇P<br />
( R = ∑<br />
i) ≈− ∑ P(<br />
R ) Aij<br />
⎜ − ⎟βi.<br />
j<br />
Rij = β<br />
v<br />
v ⎜<br />
i j Rij<br />
2 ⎟<br />
i j ∂Ri<br />
⎝ ⎠<br />
For linear pressures P() r = [ α + βi. r]<br />
( )<br />
The result is exact for<br />
arbitrary meshes !!<br />
Linear c<strong>on</strong>sistency supports our idea that<br />
<str<strong>on</strong>g>fluid</str<strong>on</strong>g> pressure forces are a discrete pressure gradient<br />
Serrano, Español, Zúñiga, J. Statistical Physics, 2005
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