• Windkessel
• Direct Numerical Simulation
• Immersed boundary method.

In cardiovascular research windkessel refers to a simplified model used to mimic
the impedance of arteries and vessels. In the context of three-dimensional (3D)
numerical simulations, the windkessel model is parameterized as a 0D system
and the resulting system of ordinary differential equations is used as a boundary
condition to a subset of the cardiovascular system. However connecting this lower
dimensional model to the 3D simulation is ill posed, since the coupling relies in
assuming the velocity and/or pressure distribution at the inlets/outlets of the 3D
system.
As an attempt to overcome the above mentioned issues, this master’s thesis
proposes a full 3D numerical solution of a windkessel system, which can be applied
as a 3D closed-loop condition in cardiovascular numerical simulations.. The
system is made of a cylindrical tube partially deformable, along with porous
and flow acceleration regions, in order to account for the resistive, capacitive
and inertial nature of the underlying vessels. The simulation employs a direct
numerical simulation of the Navier Stokes Equations for the fluid flow, whereas
immersed boundary method has been used to simulate the interaction between
fluid and the immersed bodies.
The results, in terms of pressure and flow-rate, are consistent with physiological
values and this model is promising to be incorporated in high-fidelity computational
models of the human heart.