Hodis Simona, Kallmes David F, Dragomir-Daescu Dan
Department of Radiology, Mayo Clinic, Rochester, Minnesota 55905, USA.
Department of Radiology and College of Medicine, Mayo Clinic, Rochester, Minnesota 55905, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052720. doi: 10.1103/PhysRevE.88.052720. Epub 2013 Nov 25.
Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce computational time for patient-specific hemodynamics simulations, which are used to help assess the likelihood of aneurysm rupture using CFD calculated flow patterns.
使网格密度适应流动行为具有提高求解精度的优势，同时可减少模拟域中的网格单元数量，从而缩短计算时间。一种网格自适应方法需要根据观察到的求解行为对网格密度进行连续细化，直到连续网格之间的数值误差可忽略不计。然而，这种方法耗时较长，研究人员常常忽略它。我们提出一种基于从速度场计算得到的运动学曲率和挠率，来计算复杂脑动脉瘤几何形状中用于计算流体动力学（CFD）模拟的自适应网格的网格尺寸分布的技术。流动的运动学特征与自适应网格的单元尺寸之间的关系导出了一个数学方程，用于计算流动不同区域的网格尺寸。获得自适应网格密度，使得它能够以局部较小的网格尺寸捕捉流动中更复杂的细节，而在局部较大的网格尺寸上计算不太复杂的流动特征。当前研究表明，从脑动脉瘤中的速度场计算得到的运动学曲率和挠率可用于找到复杂流动的位置，在这些位置需要细化计算网格以获得精确解。我们发现，流动的复杂性可以通过速度、涡度以及这两个向量之间的夹角来充分描述。例如，在动脉瘤泡内部、分叉处以及主要动脉转弯处，管腔内的单元尺寸需要小于动脉半径的10%，而在边界层，单元尺寸应小于动脉半径的1%，以便在相对近似误差为0.5%的范围内获得准确结果。这种量化流动复杂性和自适应重新划分网格的技术有潜力提高特定患者血流动力学模拟的结果精度并减少计算时间，这些模拟用于通过CFD计算的流动模式来帮助评估动脉瘤破裂的可能性。
