Prakash S, Ethier C R
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada M 5S 3G8.
J Biomech Eng. 2001 Apr;123(2):134-44. doi: 10.1115/1.1351807.
Computational techniques are widely used for studying large artery hemodynamics. Current trends favor analyzing flow in more anatomically realistic arteries. A significant obstacle to such analyses is generation of computational meshes that accurately resolve both the complex geometry and the physiologically relevant flow features. Here we examine, for a single arterial geometry, how velocity and wall shear stress patterns depend on mesh characteristics. A well-validated Navier-Stokes solver was used to simulate flow in an anatomically realistic human right coronary artery (RCA) using unstructured high-order tetrahedral finite element meshes. Velocities, wall shear stresses (WSS), and wall shear stress gradients were computed on a conventional "high-resolution" mesh series (60,000 to 160,000 velocity nodes) generated with a commercial meshing package. Similar calculations were then performed in a series of meshes generated through an adaptive mesh refinement (AMR) methodology. Mesh-independent velocity fields were not very difficult to obtain for both the conventional and adaptive mesh series. However, wall shear stress fields, and, in particular, wall shear stress gradient fields, were much more difficult to accurately resolve. The conventional (nonadaptive) mesh series did not show a consistent trend towards mesh-independence of WSS results. For the adaptive series, it required approximately 190,000 velocity nodes to reach an r.m.s. error in normalized WSS of less than 10 percent. Achieving mesh-independence in computed WSS fields requires a surprisingly large number of nodes, and is best approached through a systematic solution-adaptive mesh refinement technique. Calculations of WSS, and particularly WSS gradients, show appreciable errors even on meshes that appear to produce mesh-independent velocity fields.
计算技术被广泛用于研究大动脉血流动力学。当前的趋势倾向于在更符合解剖学实际的动脉中分析血流。此类分析的一个重大障碍是生成能够准确解析复杂几何形状和生理相关血流特征的计算网格。在此，我们针对单一动脉几何形状，研究速度和壁面剪应力模式如何依赖于网格特征。使用经过充分验证的纳维 - 斯托克斯求解器，通过非结构化高阶四面体有限元网格来模拟符合解剖学实际的人体右冠状动脉（RCA）中的血流。在使用商业网格生成软件包生成的常规“高分辨率”网格系列（60,000至160,000个速度节点）上计算速度、壁面剪应力（WSS）和壁面剪应力梯度。然后，通过自适应网格细化（AMR）方法生成一系列网格，并进行类似的计算。对于常规和自适应网格系列，获得与网格无关的速度场并非非常困难。然而，壁面剪应力场，尤其是壁面剪应力梯度场，要准确解析则困难得多。常规（非自适应）网格系列在WSS结果的网格独立性方面未呈现出一致趋势。对于自适应系列，需要大约190,000个速度节点才能使归一化WSS的均方根误差小于10%。在计算的WSS场中实现网格独立性需要数量惊人的节点，并且最好通过系统的求解自适应网格细化技术来实现。即使在似乎能产生与网格无关的速度场的网格上，WSS的计算，尤其是WSS梯度的计算，也显示出明显的误差。
