Generation of Computational Mesh for CFPD Simulations - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 89

real physical flow, a boundary layer develops at the wall, growing in thickness as
the fluid enters the left boundary and migrates downstream along the bottom wall of
the domain. The local thickness of the boundary layer is given as δ , which increases
with x and therefore δ = δ ( x ). It is evident that a coarse uniform mesh, in essence,
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 distribution inside the boundary layer
region.
When applying a stretched mesh as described above, care must be taken to avoid
sudden changes in the mesh size. The mesh spacing should be continuous and mesh
size discontinuities should be removed as much as possible in regions of large flow
changes, particularly when dealing with multi-block meshing of arbitrary mesh cou-
pling, non-matching cell faces or extended changes of element types. Discontinuity
in the mesh size destabilizes the numerical procedure due to the accumulation of trun-
cation 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 the divergence tendency of the numerical solution. It is
also worthwhile noting that most built-in mesh generators in commercial codes and
independent grid generation packages have the means of prescribing suitable mesh
stretching or expansion ratios (rates of change of cell size for adjacent cells).
Local mesh refinement allows the allocation of additional nodal points to resolve
important fluid flow regions' action or reduction or to remove the nodal points from
other regions where there is little or no action. However, it should be noted that
local mesh refinements are prescribed prior to the solution of the flow field being
calculated. This raises the question of whether the generated stretched grid is suf-
ficient for capturing the major fluid flow action or whether the real flow action is
far away from the intended significant flow activity to be resolved by the generated
stretched grid region, which is not known a priori . One method to overcome this
uncertainty is to refine the mesh by solution adaption . This method allows a mesh
to be refined and coarsened based not only on geometric but also numerical solution
data in regions where they are needed, thus enabling the features of the flow field to
be better resolved. This typically involves clustering nodal points in regions where
large gradients exist in the flow field. It therefore employs the solution of the flow
properties to locate the mesh nodal points in the physical flow domain. During the
course of the solution, the mesh nodal points in the physical flow domain migrate
in such a manner as to adapt to the evolution of the large flow gradients. Hence, the
actual mesh nodal points are constantly in motion during the solution of the flow field
and become stationary when the flow solution approaches some quasi-steady state
condition. An adaptive mesh is therefore intimately linked to the flow field solution
and alters as the flow field develops unlike the stretched mesh described above where
the mesh generation is completely separate from the flow field solution. For this pur-
pose, unstructured meshes are well suited especially in automating the generation of
elements such as triangular or tetrahedral meshes of various sizes to solve the critical
flow regions. Figure 4.18 shows the evolution of the adaptive mesh for fluid flowing