Conditions imposed to the grid

In order to avoid badly shaped grids, the grids must satisfy the following properties:

• The number of cells that meet at each vertex in the interior of the mesh must be at least 4 and at most 10.
• The angles inside each triangle must be smaller than a certain value. Let $\vec{a}$ and $\vec{b}$ be the tangential vectors of two faces of a triangle, then the angle $\phi$ between these two faces equals
  
  
  
    $$\cos \phi = \frac{\vec{a} \cdot \vec{b}}{\vert\vec{a}\vert\vert\vec{b}\vert}$$ (8.4)
  
  
  
  For safety, we do not allow for angles with $\cos \phi < -0.8$ or, equivalently, $\phi > 143^o$.