Generation of Computational Mesh for Haemodynamics Analysis - Computational Hemodynamics: Theory, Modelling and Applications - page 170

6.4.3 Local Refinement and Solution Adaptation

To capture critical flow regions an adequate mesh resolution is needed. Such re-
gions may include flows around obstacles that cause flow separation, attachment
and recirculation, near wall boundaries, interface shear regions, and converging and
diverging regions. These regions typically exhibit sharp flow property gradients
(e.g. velocity, pressure, temperature gradients). This has enormous impact in the
stability and convergence of the numerical procedure.
One local refinement technique we have seen is to refine the mesh close to ob-
stacle boundaries and walls. For a viscous flow bounded with solid wall boundar-
ies, clustering a large number of small cells within the physical boundary layer is
important. As an illustration, the boundary at a surface wall is shown in Fig. 6.18
to highlight the need for near wall mesh refinements. In the real physical flow, a
boundary layer develops at the wall growing in thickness as the fluid enters the left
boundary, migrating downstream along the bottom wall of the domain. The local
thickness of the boundary layer is given by δ, which increases with x and therefore
δ = δ( x ). A uniform coarse mesh misses the physical boundary layer as it develops.
In contrast, the stretched mesh with clustered nodes near the wall at the very least
catches some of the boundary layer development. It is therefore not surprising that
the accuracy of the computational solution is greatly influenced by the mesh distri-
bution inside the boundary layer region.
When applying a stretched mesh care must be taken to avoid sudden changes in
the mesh size to maintain a smooth mesh. The mesh spacing should be continuous
and mesh size discontinuities should be removed as much as possible in regions
of large flow changes. Discontinuity in the mesh size destabilizes the numerical
procedure due to the accumulation of truncation errors in the critical flow regions.
Making sure that the grid changes slowly and smoothly away from the domain
boundary as well as within the domain interior will assist in overcoming divergence
problems tendencies of the numerical calculations. It is also worthwhile noting that
most mesh generators have the means to prescribe suitable mesh stretching or ex-
pansion ratios (rates of change of cell size for adjacent cells).
Local mesh refinement includes allocation of additional nodal points to resolve
important fluid flow regions action or a removal of nodal points from other regions
where there is little or no action. However, since mesh creation occurs prior to the
solution of the flow field being calculated, where to perform local mesh require-

Fig. 6.18 Two illustrations demonstrating the influence of local refinement in the near vicinity of
the bottom wall to resolve the physical boundary layer