Boundary Layer Mesh

[Ezat Shokrani]

Dear SimVascular 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.

With respect to the first approach, how I can determine the total thickness of the boundary layer next to the wall (I mean for both steady and pulsatile flow conditions)?

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 there is a good guess for producing the boundary layer mesh with respect to this approach.

My last question for the mesh study process is that I have seen some groups take into account a ratio of 0.7 or 0.8 for element size during each step of mesh refinement. However, some groups try to adjust the element size until the number of mesh element becomes twice for each step of mesh refinement. I would like to know which one do you prefer for mesh study process.

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

Best regards,
Ezat Shokrani

[Weiguang Yang]

It might be difficult to pre-determine the boundary layer thickness and mesh resolution for blood flow simulations with a realistic geometry. Therefore you saw a variety of meshing strategies. A mesh dependence study together with previous experience is often used to determine the mesh size. The second approach seems more common in cardiovascular flow simulations. Generally, 3-5 layers of mesh with a growth factor is chosen to place denser grids near the wall and then the overall mesh size is reduced by a factor to produce several data points see how quantities of interest change with mesh size. The meshing strategies in the following studies may be useful for your problems.

http://gmsh.info/doc/preprints/gmsh_bio2_preprint.pdf
https://www.sciencedirect.com/science/a ... 0997914348
https://asmedigitalcollection.asme.org/ ... tion-in-3D

In addition, the theoretical study on pusaltile flow in curved pipes may provide a theoretical estimate.
https://www.researchgate.net/publicatio ... rved_Pipes

Hope these help.