血流模拟的浸入边界有限元法
Immersed boundary finite element method for blood flow simulation
摘要：
提出了一种高效、精确的数值求解不可压Navier-Stokes方程的浸入边界有限元方法。特别强调具有复杂几何形状的内部流动（血管系统中的血流）。IB方法对于内部流计算成本高，主要是由于大百分比的网格点位于流域之外。在这项研究中，我们采用了局部细化策略，随着域减少的方法，以减少网格，覆盖流域和增加的百分比，落在流域内的网格节点。所提出的方法利用一个高效和准确的有限元求解器与增量压力校正方案（IPCS），以及边界条件强制IB方法数值求解瞬态，不可压缩的Navier-Stokes流方程。我们验证了数值方法的准确性，使用的解析解的Poiquillille流在一个圆柱。我们进一步研究所提出的方法的准确性和适用性，通过考虑复杂的几何形状，如血管和主动脉中的血流，否则将非常难以解决的大多数IB方法的流动配置。我们的方法提供了高精度，如验证示例所示，和高效率，如通过在现成的膝上计算机上的复杂几何形状内的血流的解决方案所示。
英文摘要：
We present an efficient and accurate immersed boundary (IB) finite element (FE) solver for numerically solving incompressible Navier--Stokes equations. Particular emphasis is given to internal flows with complex geometries (blood flow in the vasculature system). IB methods are computationally costly for internal flows, mainly due to the large percentage of grid points that lie outside the flow domain. In this study, we apply a local refinement strategy, along with a domain reduction approach in order to reduce the grid that covers the flow domain and increase the percentage of the grid nodes that fall inside the flow domain. The proposed method utilizes an efficient and accurate FE solver with the incremental pressure correction scheme (IPCS), along with the boundary condition enforced IB method to numerically solve the transient, incompressible Navier--Stokes flow equations. We verify the accuracy of the numerical method using the analytical solution for Poiseuille flow in a cylinder. We further examine the accuracy and applicability of the proposed method by considering flow within complex geometries, such as blood flow in aneurysmal vessels and the aorta, flow configurations which would otherwise be extremely difficult to solve by most IB methods. Our method offers high accuracy, as demonstrated by the verification examples, and high efficiency, as demonstrated through the solution of blood flow within complex geometry on an off-the-shelf laptop computer.
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