有限要素法(FreeFem++)による三次元流体解析

1 1 2015 11 (FreeFem++) 1. (2013 ) (Blender Fluid) Fleefem++ FreeFem++ Gmsh FreeFem++ medit Paraview 2.

2 FreeFem++ Navier-Stokes equations ( ) ( ) 2 e1 ( ) ( ) e FreeFem++ FreeFem++ FreeFem++ (examples++-3d) 3.

3 FreeFem++ FreeFem++ - Gmsh ( - ) FleeFem++ FreeFem++ medit Paraview FreeFem++ ( ) ParaView - FreeFem++ 3 0 Gmsh FreeFem++ Gmsh i) TetGen ii) Buildlayers iii) readmesh3 Gmsh ( )

4 Paraview FreeFem++ medit FreeFem++ Paraview Stream Tracer Paraview FreeFem++ savevtk() .vtk Paraview Paraview 4 ( 0) ) 0 x 0 0 0 ) 4 ( , , )

5 C C t/ x, , C , , t x, , 5 Gmsh - - Gmsh - FreeFem++ medit - Gmsh - FreeFem++ - (Gmsh ) - (Gmsh ) - (Freefem++ medit ) 5 0 0 0 0 Neumann( )

6 (Dirichlet) - 800mm 1000mm ( ) FreeFem++ medit - Paraview - - (Graph-R ) - (Freefem++ medit ) 6 - m m m m -10 -11 Paraview -12 13 -13 -11 ( ) - (Paraview ) - (Paraview ) - (Graph-R) -10 ( )

7 7 m/sec m/sec ( -14) m/sec -13 ( ) -14 1 2 m/sec -15 -12 ( ) 8 ( ) -15 m m m m m -16 -16 ( 0( ) ( )) -17 m/sec 26 ( )

8 M m m m m -18 -19 20 -20 -24 -17 m/sec , -18 -16 -19 (paraView )9 -22 23 -24 -23 (v m/sec) v m/sec -28 -29 -27 ( ) -1 -20 -22 -26 -27 -21 024681012140 m/sec , 10 -27 (Graph-R )

9 6 FreeFem++ Paraview ( ) -25 (medit ) - -26 (paraView )

10 11 2004 4 22 56 FreeFem++ -Navier-Stokes - 27 .3-23