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

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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
Voronoi Ri Aij Rij Rj cij eij lim σ →0 R Distance between two neighbouring <strong>particle</strong>s ij eij Unit vector in the line joining this two <strong>particle</strong>s dr Aij = R ∫ ij χ ( ) ( ) v 2 i r χ j r 0 σ Rij dr ⎛ R i + R j ⎞ cij = ∫ χ ( ) ( ) v 2 i r χ j r ⎜r-⎟ A 0 ij σ ⎝ 2 ⎠ A ij Area joining two neighbouring cells c ij Parallel vector to the face ij giving the position of the face center of mass with respect to the medium point defined by these two cells ∂v ⎛ c i ij e ⎞ ⎛ ij cij e ⎞ ij =− Aij⎜ + ⎟+ δ ∑ ij Aij⎜ − ⎟ ∂R ⎜ j Rij2 ⎟ ⎜ i≠j Rij 2 ⎟ ⎝ ⎠ ⎝ ⎠
Page 1 and 2: A compressible <st
Page 3 and 4: Outline 1. Motivacion: Lagrangian t
Page 5 and 6: SPH Discretization of continuum hyd
Page 7 and 8: Mesoscopic fluid <
Page 11: m i dVi dt This dynamics can be und
Page 17 and 18: Spatial derivatives SDPD/Voronoi
Page 19 and 20: 2 m i Ex ( ) = ∑ + ε ( mi, Si, v
Page 21 and 22: Including thermal fluctuations ⎛
Page 23 and 24: y Comparing the performance of SDPD
Page 25 and 26: Stationary velocity profiles Disord
Page 29: Conclusions -The discrete m
Page 33 and 34: 2d implementation Structure of the
Page 35 and 36: OLD TOPOLOGY Fik Fil v1 i j v2 Time
Page 37 and 38: Properties of the non dissipative V
Page 39: SDPD Overlapping Input theory s=3 s

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

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