Computational Fluid Structure Interaction - Computational Hemodynamics: Theory, Modelling and Applications - page 146

In today's commercial CFD software, FSI can be applied with multi-physics
components required to solve haemodynamics problems. It includes the nonlinear
and anisotropic material properties into the model by user-defined functions. This
allows flow simulations of the distensible cardiovascular vessels.

5.6.2 Coupling

The interaction between the fluid and structural fields is achieved by enforcing ki-
nematic and dynamic continuity conditions at the common interface between these
domains. The kinematic continuity condition follows from the requirement that no
mass flows across the interface. For a general viscous fluid, a no-slip boundary
condition for both normal and tangential components of displacements and veloci-
ties are imposed at the interface (Donea et al. 2004; Gerstenberger and Wall 2008):

f s

dd =

=

(5.84)

s

ud

where d f and d s represent the fluid and structural displacement vectors at the
interface, u and d s are the fluid and structural velocity vectors, and n represents
the outward unit normal vector of the interface. The dynamic continuity condition
is based on force equilibrium across the interface according to principle of action
and reaction. Since the interface area is equal, this reduces to equality of traction
between both fluid and structural fields as:

σ

·n = σ ·n (5.85)

where σ represents the stress in three coordinates, the Cauchy stress tensor for
structural field; and σ is the stress tensor for the fluid field, made up of the pres-
sure and shear stress terms.
Solution strategies for FSI Coupling are mainly divided into “Monolithic” and
“Partitioned” methods. The differences between them are the method for solving
the governing equations and the interface conditions. The monolithic method com-
pletely couples the solid and fluid domains into one system of equations and solves
them directly while the partitioned approach separates the fluid and solid domains
and then solves their governing equations iteratively using two different solvers
until the solutions converge (Fig. 5.40 ).
There are benefits and deficiencies to both the monolithic and the partitioned
approaches. The obvious benefit to the monolithic approach is that, if solved, it
always produces a fully-coupled solution in a single iteration per time step. On
other hand, the biggest issue to this approach is the relatively higher computational
cost. Michler (2004) showed that in a simple one dimensional FSI problem, the