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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TOPOLOGY INFORMATION<br />
Euler<strong>the</strong>oremfor2D systemin PBC: M-F+V=0<br />
In Vor<strong>on</strong>oi<br />
F/V=3/2<br />
V=2M Vertex Matrix<br />
F=3M<br />
Faces Matrix<br />
We clasify (label) all vertex and faces and c<strong>on</strong>ectivities<br />
i j<br />
GEOMETRICAL INFORMATION<br />
Fil v2 Fjl<br />
With <strong>the</strong> topology matrixes we compute vertex coordinates, areas<br />
(lenght of <strong>the</strong> polig<strong>on</strong>al faces) vectors c and e, volumes...<br />
Of course, <strong>the</strong>y must satisfy total volume c<strong>on</strong>servati<strong>on</strong>. l<br />
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<br />
Fij i j k l V1 V2 Fik Fil Fjk Fjl V1 i j k Fij Fik Fjk<br />
TOPOLOGICAL Fik i j l RECOMBINATION<br />
... V1 ... Fik Fij Fj. Fj.<br />
Fil i l j ... V2 ... Fil Fij Flj Fl.<br />
V2 i j l Fij<br />
....<br />
Fil Fjl<br />
Fjl j l i ... V2 ... Fji Fj. Fli Fl.<br />
Because <strong>the</strong> number of faces/vertexes in PBC Vor<strong>on</strong>oi tesselati<strong>on</strong> are<br />
....<br />
c<strong>on</strong>stant, we can compute <strong>the</strong> c<strong>on</strong>nectivities of <strong>the</strong> mesh at <strong>the</strong> same<br />
time <strong>the</strong> positi<strong>on</strong>s (Vor<strong>on</strong>oi centers) follow <strong>the</strong> Lagrangian dynamics. The<br />
essential process in <strong>the</strong> topological change is given by vertex recombinati<strong>on</strong>.<br />
Fik<br />
v1<br />
Fij<br />
k<br />
Fjk
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