AuthorsO. M. Khan, K. Valen-Sendstad and D. A. Steinman
EditorsJ. D. Humphrey
TitleNumerical Resolution Requirements for Converging Wall Shear Stresses in Intracranial Aneurysms
AfilliationScientific Computing, , Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
Publication TypeProceedings, refereed
Year of Publication2014
Conference NameWorld Congress of Biomechanics Proceedings

Abstract: Background: CFD can simulate the hemodynamics forces like wall shear stress (WSS) that are known to play an important role in rupture of intracranial aneurysms. Every stone has been turned striving for more {`}patient-specific' simulations, except for numerical accuracy itself. The purpose of this study is to quantify such errors, particularly for WSS. Methods: Five refinement levels were simulated for three previously reported cases based on flow phenotype (Valen-Sendstad and Steinman, 2014): stable-sidewall (case 8), quasi-unstable- bifurcation (case 9), and unstable-bifurcation (case 16). Pulsatile simulations were performed using second-order-accurate P2-P1 (Taylor-Hood) tetrahedral elements. Finest meshes had a sac resolution of 0.055mm, 0.061mm, and 0.10mm for cases 8, 9 and 16, respectively, resulting in 4-million elements (\~32M linear tetrahedra). These finest meshes were successively coarsened by a factor of sqrt(2) with respect to side length, resulting in coarsest meshes having \~100,000 elements (\~800,000 linear tetrahedra). All meshes had four boundary layers. We used 35,000 time- steps/cycle and second-order time-stepping scheme for three reasons: 1) to avoid adding artificial numerical viscosity to stabilize the solution, 2) to eliminate temporal discretization errors, and 3) to isolate and quantify spatial discretization errors alone. Results: In contrast to conventional mesh refinement studies, we show a 3-fold decrease in effective node spacing, not simply mesh size. As a consequence, mesh sizes grew cubically. In the figure, we show normalized L2 errors for domain-averaged velocity and dome-averaged WSS at peak systole relative to the finest mesh. Although the velocity errors, a standard metric for monitoring grid convergence, appear to be within 2% error for the second-finest mesh (equivalent to \~13M linear tetrahedra), the WSS errors are an order of magnitude away from convergence. Having said this, patterns of WSS were qualitatively similar. Conclusions: High spatial resolution is required to converge WSS, even when velocity appears to be well-converged: on average, an effective mesh resolution of \~0.05mm is needed to converge WSS below \~10%. Work to be presented will also include temporal refinement study with high spatial resolution to clarify the requirements on temporal resolution, as well as the impact on popular scalar hemodynamic indices.

Citation KeySimula.simula.2890