Julia Olegivna Mikhal

Pulsatile flow in model cerebral aneurysms

We present an immersed boundary method based on volume penalization, with which pulsatile flow in a model cerebral aneurysm is simulated. The model aneurysm consists of a curved vessel merged with a spherical cavity. The dominant vortical structures arising in the time-dependent flow are discussed and the evolution of the maximal shear stress in the aneurysm is analyzed. We approximate flow properties of blood by those of an incompressible Newtonian fluid. The flow inside the aneurysm is simulated with the use of a skew-symmetric finite-volume discretization and explicit time-stepping. We focus on effects due to variations in the amplitude of the pulsatile flow as well as due to changes in the Reynolds number (Re) by studying flow at Re = 100, 250 and 500. At Re = 500 a complex time dependence in the shear stress levels is observed, reflecting the lively development of the flow in the model aneurysm in which vortices are created continuously inside the curved vessel and in the spherical cavity of the aneurysm. An increase in the amplitude of the pulsatile flow increases the shear stress levels somewhat, but at Re = 500 the flow is mainly dominated by its intrinsic unsteadiness. Reducing the Reynolds number yields a stronger contribution of the periodic pulsatile flow forcing: at Re = 100 we find a strong dominance of shear stress levels due to the forcing, while at Re = 250 the intrinsic and pulsatile unsteadiness are of comparable importance.

Development and application of a volume penalization immersed boundary method for the computation of blood flow and shear stresses in cerebral vessels and aneurysms.

A volume-penalizing immersed boundary method is presented for the simulation of laminar incompressible flow inside geometrically complex blood vessels in the human brain. We concentrate on cerebral aneurysms and compute flow in curved brain vessels with and without spherical aneurysm cavities attached. We approximate blood as an incompressible Newtonian fluid and simulate the flow with the use of a skew-symmetric finite-volume discretization and explicit time-stepping. A key element of the immersed boundary method is the so-called masking function. This is a binary function with which we identify at any location in the domain whether it is ‘solid’ or ‘fluid’, allowing to represent objects immersed in a Cartesian grid. We compare three definitions of the masking function for geometries that are non-aligned with the grid. In each case a ‘staircase’ representation is used in which a grid cell is either ‘solid’ or ‘fluid’. Reliable findings are obtained with our immersed boundary method, even at fairly coarse meshes with about 16 grid cells across a velocity profile. The validation of the immersed boundary method is provided on the basis of classical Poiseuille flow in a cylindrical pipe. We obtain first order convergence for the velocity and the shear stress, reflecting the fact that in our approach the solid-fluid interface is localized with an accuracy on the order of a grid cell. Simulations for curved vessels and aneurysms are done for different flow regimes, characterized by different values of the Reynolds number (

Application of an immersed boundary method to flow in cerebral aneurysms and porous media

Re

Tomographic immersed boundary method for permeability prediction of realistic porous media: Simulation and experimental validation

). The validation is performed for laminar flow at

Bounding solutions for cerebral aneurysms

Re=250

Immersed boundary method for pulsatile transitional flow in realistic cerebral aneurysms

, while the flow in more complex geometries is studied at