## Team for Advanced Flow Simulation and Modeling |

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## Wall Shear Stress and Oscillatory Shear Index Calculations With Refined MeshesWe report the wall shear stress (WSS) and oscillatory shear index (OSI) calculations we carried out with different levels of fluid mechanics mesh refinement, using the special techniques we developed for WSS and OSI calculations. The lumen geometry used here was provided by Dr. Ryo Torii (University College London). It was extracted from the computed tomography model of a bifurcating segment of the middle cerebral artery of a 67 year-old female with aneurysm. The arterial wall (i.e. the structural mechanics part of the problem) is modeled with the continuum element made of hyperelastic (Fung) material. The numerical methods used in this computation were introduced and implemented on parallel computing platforms by the T*AFSM. The set of numerical methods introduced by the T*AFSM over the years and used in this computation includes the DSD/SST formulation [1-4], the quasi-direct FSI method [5, 6], the stabilized space-time FSI (SSTFSI) technique [7], and special techniques for arterial FSI computations [8-11], a multiscale sequentially-coupled arterial FSI technique [12], and special techniques for WSS and OSI calculations [13]. The lumen geometry was used earlier in simulations reported in [14, 15]. The inflow volumetric flow rate is calculated (see [13]) from the maximum-velocity waveform used in [14]. The inflow volumetric flow rate is shown in Fig. 1. The inflow velocity profile (in space and time) is calculated (see [11]) based on this volumetric flow rate by using a special mapping technique introduced in [11]. The traction condition imposed at the outflow boundary during the cardiac cycle is based on a normal blood pressure profile, which is calculated (see [11]) by using the Windkessel model and the inflow volumetric flow rate. The pressure profile is shown in Fig. 1. We use a variation of the "estimated zero-pressure arterial geometry" method that was introduced in [9]. In this variation (see [11]), we use variable wall thickness for the artery. The zero-pressure configuration and the wall thickness normalized by the wall thickness at the inflow can be seen at Cerebral Aneurysm -- High-Resolution Wall Shear Stress. The structural mechanics meshes are shown in Fig. 2. One of the special arterial FSI techniques used in the computation is generating layered, high-refinement meshes near the arterial walls to improve the boundary layer resolution (see [10, 11]). In the computations reported here, three fluid mechanics meshes are used: a coarse mesh, a medium mesh with such layered, high-refinement zones, and a fine mesh with higher refinement also over the arterial wall. The coarse and medium meshes have the same triangular mesh at the arterial wall. All three fluid mechanics meshes at the inflow plane are shown in Fig. 3. Fluid-structure interface for the fluid mechanics meshes is shown in Figs. 4 and 5. The layered, high-refinement meshes near the arterial wall give us higher-resolution WSS values (see Figs. 6-9). For more details on these computations, see [13].
## References
1. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", |