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

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TOPOLOGY INFORMATION Eulertheoremfor2D systemin PBC: M-F+V=0 In Voronoi F/V=3/2 V=2M Vertex Matrix F=3M Faces Matrix We clasify (label) all vertex and faces and conectivities i j GEOMETRICAL INFORMATION Fil v2 Fjl With the topology matrixes we compute vertex coordinates, areas (lenght of the poligonal faces) vectors c and e, volumes... Of course, they must satisfy total volume conservation. l a\b b=1 b=2 b=3 b=4 b=5 b=6 b=7 b=8 b=9 b=10 a\b b=1 b=2 b=3 b=4 b=5 b=6 Fij i j k l V1 V2 Fik Fil Fjk Fjl V1 i j k Fij Fik Fjk TOPOLOGICAL Fik i j l RECOMBINATION ... V1 ... Fik Fij Fj. Fj. Fil i l j ... V2 ... Fil Fij Flj Fl. V2 i j l Fij .... Fil Fjl Fjl j l i ... V2 ... Fji Fj. Fli Fl. Because the number of faces/vertexes in PBC Voronoi tesselation are .... constant, we can compute the connectivities of the mesh at the same time the positions (Voronoi centers) follow the Lagrangian dynamics. The essential process in the topological change is given by vertex recombination. Fik v1 Fij k Fjk
OLD TOPOLOGY Fik Fil v1 i j v2 Time 1 k Fij l Fjk Fjl Fik Fil CHECK TOPOLOGY for each FACE Use old topologic information. CIRCUMCIRCLE CRITERIA i OK!! v1 v2 k l Time 2 Fjk j Fij Fjl WRONG <strong>particle</strong> k inside!! Fik Fil i k Fkl v1 v2 l Fjk Fjl WRONG <strong>particle</strong> l inside!! Time 3 CHANGE MFACES AND MVERTEX!! j
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 and 12: m i dVi dt This dynamics can be und
Page 13 and 14: Voronoi Ri Aij Rij Rj cij eij lim
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: 2d implementation Structure of the
Page 37 and 38: Properties of the non dissipative V
Page 39: SDPD Overlapping Input theory s=3 s

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