Biomedical Engineering Reference
In-Depth Information
(a) U mesh
(b) BL mesh
Fig. 13.8.
Definition of mesh size
h
and the mesh size normal to the wall
h
n
for (a) an unstructured
tetrahedral mesh and (b) a boundary layer mesh. For this example, we have taken a value of
h
n
=
h
/
4
The vessel radius is evaluated in Gmsh as the Euclidian distance to the centerlines
(see Fig. 13.7a) which are extracted with the open source VMTK library [2, 3]. We
consider two different meshes (see Fig. 13.8): (a) a fully unstructured mesh (called
U mesh) of size
h
and (b) a boundary layer mesh (called BL mesh) with 4 layers
having a mesh size normal to the wall
h
n
=
h
/
4 and filled with tetrahedra of mesh
10
5
tetrahedra.
We have also build a U mesh that has a similar mesh size than the BL mesh at the
boundary (mesh size of
h
10
4
size
h
. The U mesh has 6
.
tetrahedra while the BL mesh has 2
.
10
6
tetrahedra.
The blood flow simulation is conducted over a time-span of four cardiac cycles
with a realistic time-dependent inlet blood flow rate. Unlike in the steady case, flow
rate boundary conditions are prescribed [31] at the different outlets with a magnitude
of respectively 15%
/
4). This fine U mesh is made of 1
.
5
.
10% and 65% of the inlet flow rate. We kept the same
settings for the linear solver as in the steady case, except for the ILU preconditioner
which was replaced by an algebraic multigrid preconditioner (implemented in LifeV
as a wrapper to the ML package within the Trilinos library
6
). The coarse multigrid
level was resolved with LU decomposition, and at the fine level Chebychev iterations
were used as smoother.
Fig. 13.10 shows a mesh convergence analysis of the mean WSS at section
AA
for those two different types of meshes We also compare the shear vector forces at
peak systole along the circumference at section
AA
(see Fig. 13.7) computed on both
meshes. The results obtained on the boundary layer mesh (Fig. 13.9) show higher
value of the wall shear stress than on unstructured mesh. This is due to the fact that
for the fully unstructured meshes, the mesh adjacent to the wall is not fine enough to
,
10%
,
6
http://trilinos.sandia.gov
