Biomedical Engineering Reference
In-Depth Information
Fig. 16.4
Registration of
TCPC surface mesh (
light
gray
) within regular,
background Cartesian grid
16.2.3 Computational Fluid Dynamics
The final critical component of the surgical planning tool set is the means to pre-
dict hemodynamic outcomes for all virtually designed connection options. For this,
computational fluid dynamics (CFD) solvers play a central role. The subsequent
sections provide descriptions of the important considerations inherent to such mod-
eling, followed by selected results from preliminary experiences.
16.2.3.1 Solver Description
It is important to note that any validated computational fluid solver can be used
to yield the needed results for these analyses; however, the program presently de-
scribed has the advantage of simplifying the process of generating the discretized
computational mesh. In cases where there are a large number of possible anatomic
solutions to evaluate, this advantage is non-trivial.
The solver is based on the sharp-interface immersed boundary approach of
Gilmanov and Sotiropoulos (
2005
). This method, rather than requiring a dense,
high quality mesh of volume elements throughout the computational domain, only
requires the boundary (i.e., the walls of the TCPC) to be discretized with two-
dimensional triangular elements. This surface is then immersed and registered
within a regular Cartesian grid (Fig.
16.4
) to be segregated into fluid nodes (those
falling within the boundaries), 'immersed boundary' (IB) nodes (nodes within the
boundaries but immediately adjacent to the sharp-interface of the wall), and wall
nodes (those external to the boundary). The 3D, unsteady incompressible Navier-
Stokes equations must then only be solved on the internal fluid nodes (discretized in
a hybrid staggered/non-staggered layout), with the wall boundary conditions (typi-
cally, the no-slip condition), imposed iteratively on the IB nodes. As described by
de Zélicourt et al. (
2009
) this method is further simplified by recasting the problem
into an unstructured Cartesian grid to reduced the required memory overhead of the
discarded wall nodes.
