Biomedical Engineering Reference
In-Depth Information
Tetrahedral cells are also prone to high aspect ratios that affect the skewness of the
cell. Additionally tetrahedral cells can be difficult to align with the flow direction.
These two problems can impede convergence and lead to artificial errors in the so-
lution, known as
numerical diffusion
. This common source of error is also called
false diffusion
because it is a product of numerical error and does not represent a
physically occurring phenomenon. A few techniques may be applied to minimise the
likelihood of false diffusion such as choosing higher order discretisation schemes
(discussed later in Chap. 7) and increasing the resolution of the mesh.
4.4
Mesh Generation
4.4.1
Mesh Design Strategy and Quality
Generating a quality mesh is by no means a trivial exercise. In fact, it can be seen
as much of an art form as it is technical, and often a user's experience in mesh
designs dictates the final mesh quality. To begin, the user should create an initial
coarse mesh for evaluating and testing the setup of a particular CFD problem (i.e. to
use a small number of mesh elements in relation to the final model which will have
a significantly higher number of elements). This strategy allows the computational
model to evaluate the specific computer code's storage and running time. More
importantly, a suitable coarse mesh allows a number of “test-runs” to be carried out
in quick turnaround time to assess the convergence or divergence behaviour of the
numerical calculations, and the application of physical models (e.g. different drag
coefficient). When the numerical model is setup correctly and is suitable, and the
solution is found to be converging, mesh refinement within the flow domain can then
be undertaken to achieve a more accurate CFD solution. If the solution is diverging,
the user needs to investigate the problems arising during the numerical calculations.
Some possible sources of errors can be attributed to
physical modelling
and
human
errors. During the testing phase, it is not recommended that a fine mesh be used
because this could take hours or days, only to find the solution is diverging or that
the physical model was applied incorrectly.
The quality of a generated mesh depends on the consideration of the cell shape
based on its
aspect ratio
,
skewness
, and
warp angle
. A quadrilateral cell having a
mesh spacing of
x
and
y
and an angle of
θ
between the grid lines of a cell is shown
in Fig.
4.14
. The grid
aspect ratio
of the cell is defined as
AR
=
y
/
x
. Large aspect
ratios should always be avoided in important flow regions inside the computational
domain (e.g. jets, flow separation, attachment and recirculation) as they can degrade
the solution accuracy and may result in poor iterative convergence (or divergence)
depending on the computational flow solver during the numerical computations.
It is recommended that the
AR
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
y
direction, then the first mesh
requirement is to resolve the velocity gradient in the
y
-direction. This means that
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