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

机译：颅内动脉瘤的血流动力学建模：基于有限元和有限体积方案的CFD求解器精度比较

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摘要

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two 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 two representative CFD solvers in simulating flow in a patient-specific IA 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 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths.
机译：基于图像的计算流体动力学（CFD）已显示出潜力，可协助颅内动脉瘤（IAs）的临床管理，但由于缺乏准确性评估和敏感性分析，因此在临床实践中一直缺乏采用。为了对流动方程进行数值求解，CFD求解器通常依赖于两种空间离散方案：有限体积（FV）和有限元（FE）。由于通过不同的方法可以获得越来越精确的数值解，因此无法直接比较FV和FE公式的准确性和计算成本。为此，在本研究中，我们在模拟特定于患者的IA模型中的流量时，对两个代表性的CFD求解器进行了基准测试：（1）ANSYS Fluent，基于商用FV的求解器，以及（2）VMTKLab multidGetto，不连续的Galerkin（dG）有限元基于的求解器。通过增加空间网格分辨率（134k，1.1m，8.6m和68.5m四面体网格），可以提高FV求解器的精度。通过增加基础134k四面体单元网格上的多项式的阶数（第一，第二，第三和第四阶），可以提高dGFE求解器的精度。来自最佳FV和dGFE近似值的解决方案用作误差量化的基准。平均而言，对于[0,125] cm / s的速度幅值场，次优近似值的速度误差约为1cm / s。结果表明，与FV相比，高阶dGFE在每个自由度上提供了更高的精度，但在每个Jacobian非零输入下提供了更差的精度。速度误差的交叉比较证明了两个求解器到相同数值解的渐近收敛性。但是，欠解析速度场之间的差异表明，沿着不同的路径可以达到网格独立性。

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