A compressible fluid particle model based on the Voronoi ...

Reversible <strong>fluid</strong> <strong>particle</strong> <strong>model</strong>
dRi
() t = Vi
dt
dv
dt
i
dV
i m i
dt
dS
dt
i
=
∑
j
=
() t = 0
∂ v
∂R
∑
j
i
j
iV
∂ v
∂R
j
i
j
p
j
Euler equations (Inviscid <strong>fluid</strong>)
dρ(,) r t
dv( r=−
, t)
ρ(,)
r t ∇⋅v(,)
r t
dt = v( r,
t)
∇ ⋅v(
r,
t)
dt
dgr (,) t
=−gr (,) t ∇ ∇⋅v(,) rt − ∇
∇P(,)
rt
dtdv
( r,
t)
m = −v(
r,
t)
∇P(
r,
t)
ds(,) r t dt
=−s(,) r t ∇⋅v(,)
r t
dt
dS( r,
t)
dt
Discrete variables ... In continuum Continuum extensive fields fields
Discrete version
of
continuum operators
.
=
Specific Volume, momentum and Entropy
ANALOGY
Gradient
Divergence
−
0
∂v
f ≈ v∇f ∑ R
j
j
j ∂ i
∂v
∑
i f j
j ∂Rj
⋅ ≈v∇⋅
f