Biomedical Engineering Reference
In-Depth Information
The Eulerian frame, on the other hand, is based on the idea that material point
moves with respect to fixed computational grid. This allows large distortions in
the continuum motion to exist in computational domain. It is widely used in fluid
dynamics where large movements in the continuum fluid is handled with relative
ease, but generally at the expense of precise interface and free surface detection. It
also leads to a decrease in the accuracy of solution.
The Arbitrary Lagrangian-Eulerian frame is developed to incorporate the desir-
able feature of Lagrangian and Eulerian frame. In this frame of reference, the com-
putational grid can either be fixed or moved with continuum. This is the reason why
ALE can prove to have large distortion and also the accuracy of solution is not de-
graded. When using the ALE technique in engineering simulations, the computation-
al mesh inside the domains can move arbitrarily to optimize the shapes of elements,
while the mesh on the boundaries and interfaces of the domains can move along with
materials to precisely track the boundaries and interfaces of a multi-material sys-
tem. ALE-based finite element formulations can reduce to either Lagrangian-based
finite element formulations by equating mesh motion to material motion or Eulerian-
based finite element formulations by fixing mesh in space. Therefore, one finite ele-
ment code can be used to perform comprehensive engineering simulations, including
heat transfer, fluid flow, fluid-structure interactions and metal-manufacturing.
6.4
Mesh Generation
6.4.1
Mesh Quality
Mesh quality depends on the cell shape based on its
aspect ratio
,
skewness
,
warp an-
gle,
and
smoothness
. 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.
6.15
. The cell
aspect ratio
is defined as
AR
=
∆
y
/
∆
x
. Large aspect ratios should always be avoided in important
flow regions (e.g. jets, flow separation, attachment and recirculation) as they de-
grade the solution accuracy and result in poor iterative convergence (or divergence)
depending on the computational flow solver during the numerical computations.
Fig. 6.15
Definition of mesh spacing,
∆
x
and
∆
y
and an angle of θ between the grid lines of a
quadrilateral cell, and examples of high aspect ratio elements
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