224
V. Kurtcuoglu et al.
Once the boundary conditions are in place, initial conditions in the form of
velocity and pressure have to be defined throughout the computational domain.
If results from previous calculations, usually on a coarse computational grid, are
available, they can be extra- or interpolated to the new grid as initial conditions.
Otherwise, zero initial velocity and constant pressure are usually applied. Since the
corresponding fluid dynamic state will not match to the actual flow field, transient
calculations are performed over a few cardiac and, if considered, respiratory cycles,
until no significant difference in the state between two subsequent cycles can be
observed. Depending on the CFD solver and the numerical method employed, a
constant initial condition may render the calculations unstable. In that case, the
magnitudes or amplitudes of the applied boundary conditions can be scaled down
initially and increased to their actual values over several cycles.
9.2.4 Calculating the Flow
A wide range of CFD tools suitable for CSF dynamics modelling exist, from userfriendly commercial software [9, 10, 12, 52–54] to free open-source codes [33–35,
53], each with their unique strengths and weaknesses. CFD tool choice depends
primarily on the complexity of the envisioned model, licensing cost and familiarity
with the tool. High complexity in terms of model size calls for software that can
utilize HPC resources. While most relevant CFD tools offer parallel processing, the
comparably low parallel efficiency of traditional finite volume and element codes
is an important limiting factor. This issue is exacerbated by the continuing trend
towards larger numbers of cores per CPU but only slow increase in clock speed
and available memory per core. As a result, approaches that offer better parallel
scaling, such as lattice Boltzmann methods, have seen rising interest in the recent
years. The speed increase with such methods is particularly relevant for transient
calculations.
In the vascular area, steady-state calculations of blood flow are employed when
details of the flow field do not need to be captured, for example, to estimate
average wall shear stress distribution or other similar parameters linked to long-term
processes such as atherosclerosis [55]. In contrast to haemodynamics, CSF flow
has a much stronger oscillatory component compared to its net flow, which makes
steady-state simulations typically not applicable. For transient CFD simulations,
the proper temporal discretization step size has to be chosen, which will depend
on the expected flow frequencies (see Sect. 9.2.3), the discretization scheme, the
spatial resolution of the computational grid and the CFD solver. Commonly used
time step sizes in the CSF space are on the order of 1 ms [32]. As with the grid
independence study (Sect. 9.2.2), time step independence of the acquired solution
must be ensured.
CSF flow is generally considered laminar. Recent studies employing direct
numerical simulation (DNS) have challenged this assumption [31, 35], raising the
question if currently used time step sizes and grid resolutions are adequate and
V. Kurtcuoglu et al.
Once the boundary conditions are in place, initial conditions in the form of
velocity and pressure have to be defined throughout the computational domain.
If results from previous calculations, usually on a coarse computational grid, are
available, they can be extra- or interpolated to the new grid as initial conditions.
Otherwise, zero initial velocity and constant pressure are usually applied. Since the
corresponding fluid dynamic state will not match to the actual flow field, transient
calculations are performed over a few cardiac and, if considered, respiratory cycles,
until no significant difference in the state between two subsequent cycles can be
observed. Depending on the CFD solver and the numerical method employed, a
constant initial condition may render the calculations unstable. In that case, the
magnitudes or amplitudes of the applied boundary conditions can be scaled down
initially and increased to their actual values over several cycles.
9.2.4 Calculating the Flow
A wide range of CFD tools suitable for CSF dynamics modelling exist, from userfriendly commercial software [9, 10, 12, 52–54] to free open-source codes [33–35,
53], each with their unique strengths and weaknesses. CFD tool choice depends
primarily on the complexity of the envisioned model, licensing cost and familiarity
with the tool. High complexity in terms of model size calls for software that can
utilize HPC resources. While most relevant CFD tools offer parallel processing, the
comparably low parallel efficiency of traditional finite volume and element codes
is an important limiting factor. This issue is exacerbated by the continuing trend
towards larger numbers of cores per CPU but only slow increase in clock speed
and available memory per core. As a result, approaches that offer better parallel
scaling, such as lattice Boltzmann methods, have seen rising interest in the recent
years. The speed increase with such methods is particularly relevant for transient
calculations.
In the vascular area, steady-state calculations of blood flow are employed when
details of the flow field do not need to be captured, for example, to estimate
average wall shear stress distribution or other similar parameters linked to long-term
processes such as atherosclerosis [55]. In contrast to haemodynamics, CSF flow
has a much stronger oscillatory component compared to its net flow, which makes
steady-state simulations typically not applicable. For transient CFD simulations,
the proper temporal discretization step size has to be chosen, which will depend
on the expected flow frequencies (see Sect. 9.2.3), the discretization scheme, the
spatial resolution of the computational grid and the CFD solver. Commonly used
time step sizes in the CSF space are on the order of 1 ms [32]. As with the grid
independence study (Sect. 9.2.2), time step independence of the acquired solution
must be ensured.
CSF flow is generally considered laminar. Recent studies employing direct
numerical simulation (DNS) have challenged this assumption [31, 35], raising the
question if currently used time step sizes and grid resolutions are adequate and