Generation of Computational Mesh for Haemodynamics Analysis - Computational Hemodynamics: Theory, Modelling and Applications - page 168

Fig. 6.16 An example of a highly skewed triangular cell, and a quadrilateral cell. a skewed trian-
gular cell b skewed quadrilateral cell

The AR should be maintained within the range of 0.2 < AR < 5 within the interior
region, if possible. For near wall boundaries the condition for AR can, however, be
relaxed. If the fluid flow is in the x direction, then the first mesh requirement is to
resolve the velocity gradient in the y -direction because of the thin boundary layer.
To avoid poor AR, the ∆ x mesh spacing should also be small enough to produce an
AR within the suitable range. Such consideration can assist in possibly alleviating
convergence difficulties and enhancing the solution accuracy especially where ap-
propriately resolving the wall boundary layers is necessary.
Mesh distortion or skewness is measured by determining the angle θ between the
mesh lines (Fig. 6.16 ). For triangles and tetrahedrals, the skewness can be quanti-
fied by using the ideal equilateral triangle as a reference by the equation

Ideal Cell − Actual Cell

skewness = .

Ideal Cell

For quadrilateral cells, minimal distortion, mesh lines should be at an angle θ of
approximately 90 degrees (orthogonal). If the angle is θ < 45° or θ > 135°, the mesh
becomes skewed and lead to deterioration in the computational results or numerical
instabilities.
For an unstructured mesh warp angles measuring between the surfaces' normal
to the triangular parts of the faces should be no greater than 75 degrees, indicated
by the angle  in Fig. 6.17 . Cells with large deviations from the co-planar faces
can lead to serious convergence problems and deterioration in the computational
results. This occurs when trying to cluster tetrahedrals in wall boundaries to resolve
the thin fluid boundary layers. Whenever possible, tetrahedral elements should be
avoided in wall boundary layers and instead prismatic or hexahedral cells are pre-
ferred. In any case, warp angle problems can be overcome by grid smoothing to
improve the element warp angles.
Mesh elements should also exhibit gradual or smooth change in sizes from one
to another. Adjacent cells should be less than 20 % in size difference as any large
sudden increase or decrease in adjacent cells causes difficult convergence of the
solution.