Biomedical Engineering Reference
In-Depth Information
In some cases, applying peak values on the target side of the interface will initi-
ate oscillatory convergence or even divergence within and between the coupled
solvers. Therefore, the target side data may be ramped from the final value observed
in the previous coupling step to the peak value during the initial coupling interac-
tions within the current step by using under-relaxation factors.
The order of which solver is initiated first also affects the FSI solution stability.
In general, the fluid analysis should be processed first since the it causes the struc-
ture to deform To check the convergence the structural solver, the fluid solver and
the data exchanged across the interface have to all converge to the a prescribed re-
sidual limit. For a full transient simulation, convergence should take place at every
time step for the results to be accurate.
Sometimes, it is difficult to get a coupled simulation to initiate, or you want to
check the setup before conducting a multi-field simulation. Then it is recommend-
ed to run the fluid solver and the structure solver separately for trial simulations.
For example, if you want to get an impression or preliminary results of the struc-
tural deformation, a characteristic pressure load roughly reflecting the real pressure
exerted by the blood flow can be loaded to the same location where you have de-
fined the FSI interface. Then, run the structural solver to solve just the mechanical
component with this dummy pressure load. To test the fluid component of the FSI
coupling system, a fixed or time-dependent mesh displacement wall boundary can
be used to replace the mesh displacement settings at the FSI interface. Then run
the fluid solver separately to check the fluid solver's setup and perform debugging
if necessary.
5.7
Summary
Fluid structure interaction modelling is the merging of fluid dynamics and solid
mechanics. It is therefore important to be familiar with both sets of equations that
govern fluid flow and structural deformation. This chapter presented mass conser-
vation, and the momentum equations with a focus on understanding the individual
terms in the equations. This includes understanding the fundamental principle of
mass conservation, the local acceleration, advection, pressure, diffusion, and body
forces that act on the blood and that it exerts during its flows. An introduction to
turbulence modelling was also given with an emphasis on understanding the char-
acteristics of turbulence and practical guidelines on turbulence model selection for
internal blood flows.
For the structural equations a review of the basics of solid mechanics was given
which linked the material properties of elasticity, stress, and strain with its structural
dynamics to yield the three fundamental forces of inertia, damping, and stiffness.
The composition of the arterial walls plays a major role in its elastic properties. The
relative tissue composition of endothelium, elastic tissue, smooth muscle, and fi-
brous tissue was shown for different artery types and how this influences the ability
to deform during pressure loadings from the blood flow.
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