Boundary layer mesh

12 Jun 2021

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Dear Nektar++ developers,

I am working on numerical simulation of blood flow in arteries. The flow
regime of my case study is laminar. In addition to obtaining velocity and
pressure field, the evaluation of shear rate and WSS for this case is also
important for me. Therefore, in addition to using tetrahedral elements as
core mesh, I am going to employ prism layers for resolving the boundary
layer next to the wall.

I have seen, in the literature, that there are two approaches for producing
the boundary layer mesh that most groups use them. Firstly, some groups
consider a constant total thickness for boundary layer mesh. This means
that during the mesh study process, they do not change the overall
thickness but they try to increase the number of layers. Secondly, other
groups consider a constant number of layers for the boundary layer mesh
(e.g. three layers for the coarse mesh) during the mesh study and when they
refine the mesh in each step, the element size of each layer decreases. As
a result, the total thickness of boundary layer mesh decreases too.
Meanwhile, I have encountered some questions related to these approaches
for producing boundary layer mesh.

I have seen in articles related to the blood flow simulation which is done
using Nektar++, p-refinement method has been used for mesh study process
which I think this mimics the first approach. My question is that how I can
calculate the total thickness of the boundary layer mesh (both steady and
pulsatile flow conditions) through the mesh study.

Related to the second approach, I have seen different research teams have
various opinions for constructing the boundary layer mesh even for the
cases with similar geometry and flow conditions. For example, different
groups produce boundary layer mesh with a range of 3 to 20 layers. In
addition, some consider a constant thickness for “each” layer (with no
growth factor). However, others try to use a growth factor to vary the
thickness of each layer. Even, different groups use a variety of core
element size to boundary layer size ratio to construct the mesh. I know
that this depends on the case study but they did not mention any reason for
their choices. I would like to know whether or not there is a rule of thumb
for this process or if there is a good guess for producing the boundary
layer mesh with respect to this approach.

I would be wondering if you could guide me on these issues.

Best regards,

Ezat Shokrani,

Ezat Shokrani

Mahdi Erfanian Nakhchi

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