Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms, but its adoption in the clinical practice has been missing, partially because of lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations, CFD solvers generally rely on 2 spatial discretization schemes: finite volume (FV) and finite element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study, we benchmark 2 representative CFD solvers in simulating flow in a patient-specific intracranial aneurysm model: (1) ANSYS Fluent, a commercial FV-based solver, and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m, and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third, and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1 cm/s for a [0,125] cm/s velocity magnitude field. Results show that high-order dGFE provides better accuracy per degree of freedom but worse accuracy per Jacobian nonzero entry as compared with FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between underresolved velocity fields suggests that mesh independence is reached following different paths.