Transitional flow in intracranial aneurysms – A space and time refinement study below the Kolmogorov scales using Lattice Boltzmann Method

Abstract

Most Computational Fluid Dynamics (CFD) studies of hemodynamics in intracranial aneurysms are based on the assumption of laminar flow due to a relatively low (below 500) parent artery Reynolds number. A few studies have recently demonstrated the occurrence of transitional flow in aneurysms, but these studies employed special finite element schemes tailored to capture transitional nature of flow. In this study we investigate the occurrence of transition using a standard Lattice Boltzmann method (LBM). The LBM is used because of its computational efficiency, which in the present study allowed us to perform simulations at a higher resolution than has been done in the context of aneurysms before. The high space-time resolutions of 8 µm and 0.11 µs resulted in nearly 1 × 10 9 cells and 9 × 10 6 time steps per second and allowed us to quantify the turbulent kinetic energy at resolutions below the Kolmogorov scales. We perform an in-depth space and time refinement study on 2 aneurysms; one was previously reported laminar, while the other was reported transitional. Furthermore, we investigate the critical Reynolds number at which the flow transitions in aneurysms under time constant inflow conditions.

Direct numerical simulation of transitional hydrodynamics of the cerebrospinal fluid in Chiari I malformation: The role of cranio‐vertebral junction

“…The dissipation in Patient2 is higher as sketched by u η , which demands for higher spatial and temporal resolutions. The t + is always lesser than 1.0 because of the intrinsically low δ t in the LBM algorithm . A review by Moin and Mahesh suggested that the smallest length scale that needs to be resolved for an accurate DNS of turbulent flows is required to be .…”

“…The Kolmogorov length, time, and velocity scales are then respectively estimated as On the basis of these scales, the quality of the spatial and temporal resolutions of a simulation is estimated by computing the ratio of δ x and δ t against corresponding Kolmogorov scales, i.e., We remark that the Kolmogorov theory generally applies to a flow with infinitely large Reynolds number, when the turbulence is homogeneous and isotropic in nature. Our analysis is based on this theory for a surrogate estimate of the quality of the spatial and temporal resolutions, as has been done in previous works …”

“…Motivated by the aforementioned observations, the novelty of the present research is to investigate the possibility of transitional CSF hydrodynamics in detail, which is accomplished by performing fully resolved direct numerical simulations (DNS) on subject‐specific models of 1 control subject (Control) and 2 CMI patients (Patient1 and Patient2). The lattice Boltzmann method (LBM) is used for the simulations because of its suitability in DNS of moderate Re flows in complex anatomical geometries and its appreciable compute efficiency on modern supercomputers . Simulations with almost 1 billion cells are conducted on the SuperMUC and the Hazel Hen , which are national supercomputers installed in Germany.…”

Transitional hemodynamics in intracranial aneurysms — Comparative velocity investigations with high resolution lattice Boltzmann simulations, normal resolution ANSYS simulations, and MR imaging

“…Because of the failure to recognize this phenomenon in many previous computational studies, there is now considerable interest in evaluating (1) what CFD methods have accounted for this shortcoming and (2) how future studies must be tailored so that there is adequate resolution for their detection and analysis. [14][15][16] Computation of hemodynamic quantities becomes challenging in such a flow regime due to large and unpredictable temporal variations in flow characteristics. 17 In spite of recent developments in volumetric phasecontrast magnetic resonance angiography (PC-MRA) which allow instantaneous 3D velocity encoding, these techniques are still suboptimal to capture the transitional flow phenomenon.…”

“…[18][19][20] Furthermore in magnetic resonance (MR), even minor fluctuations in flow can lead to intravoxel dephasing where proton spins within the resolution cell become randomly oriented such that the accuracy of velocity measurements is significantly affected. 21 Computational hemodynamic modeling when performed on supercomputers, though capable of resolving the smallest spatial structures at minutest temporal scales, must be appropriately resolved according to the underlying flow regime, 14,15 and the stabilization schemes that might suppress the onset of flow-transition must be appropriately employed. 15 Currently, this as well as the limited computational availability makes it impossible to apply the insights into such highly resolved (HR) simulations in a clinical setting, though high resolution hemodynamic simulations remain a useful tool for basic and clinical research.…”