Numerical simulations of flows in cerebral aneurysms using the lattice Boltzmann method with single- and multiple-relaxation time collision models

Lattice Boltzmann simulations of flows in TOF-MRA-based cerebral aneurysm models are carried out using the single-, two- and multiple-relaxation time collision models, SRT, TRT and MRT, to investigate the effects of the collision model on predicted velocity fields in the aneurysms. The non-Newtonian characteristics of blood are accounted for by using the Casson model, whereas a simulation with the Newtonian viscous stress model is also carried out to investigate the effects of the viscous stress model on predicted velocity and wall shear stress distributions. Four cerebral aneurysm models are used in the simulation. The shapes of cerebral arteries are extracted from TOF-MRA data as STL meshes, and the level set function representing the artery wall is reconstructed from the STL mesh data. By making use of the level set function in the interpolated bounce-back scheme, the complex structures of arteries having aneurysms can be easily dealt with in the LB framework. As a result, the following conclusions are obtained: (1) the SRT can give reasonable predictions comparable to the MRT, provided that the spatial resolution is high enough; otherwise numerical errors can be large and numerical instabilities take place, (2) numerical errors in velocity is apt to take place in the near aneurysm wall region due to a small velocity scale, (3) although the TRT is less stable than the MRT, predictions of the TRT under stable numerical conditions are almost the same as those of the MRT, and (4) although the Bingham number effect on the flow structure is small, the mean wall shear stress may change over several percent, depending on the configuration of the aneurysm and the main blood flow, by neglecting the non-Newtonian nature of blood.