The graph shows that even a relatively coarse polyhedron mesh which requires 1.6 hr to converge approaches a grid-independent solution. A finer mesh that needs 6 hr to converge provides a solution with an acceptably small error. With tetrahedral meshes, results overshoot the grid-independent solution. Only a very fine mesh that needs over 33 hr to converge provides a solution with the same acceptably small error.

The graph shows that even a relatively coarse polyhedron mesh which requires 1.6 hr to converge approaches a grid-independent solution. A finer mesh that needs 6 hr to converge provides a solution with an acceptably small error. With tetrahedral meshes, results overshoot the grid-independent solution. Only a very fine mesh that needs over 33 hr to converge provides a solution with the same acceptably small error.


In 1887, Lord Kelvin found that a 14-sided polyhedron (tetrakaidecahedron) would most efficiently pack bubbles into foam when all bubbles are of equal size. In 1994, physicists Denis Weaire and Robert Phelan found that a mixture of 12 and 14-sided polyhedrons partition space 3% more efficiently than Kelvin's foam.

The recent polyhedral meshes actually use an unrestricted number of faces, so they fill space in most efficiently. In fact, for a given resolution level, a mesh of polyhedral cells has fewer faces than a mesh of any other cell type.

CD-adapco Inc., cd-adepco.com