粘弹性流动中浸入边界法的基准测试
Benchmarking the Immersed Boundary Method for Viscoelastic Flows
AI总结：
本文通过二维算例和流变实验，对浸入边界法在Oldroyd-B和Rolie-Poly粘弹性流动中的精度与收敛性进行基准测试，并与有限元、有限体积法比较，给出正则化delta函数和拉格朗日网格间距的推荐选择。
摘要：
我们提出并分析了一系列关于浸入边界（IB）方法应用于流经和绕过非平凡静止几何体的粘弹性流动的基准测试。IB方法广泛用于生物流体动力学以及其他将结构浸入流体中的建模场景的模拟。尽管IB方法最常用于模拟粘性不可压缩流体系统，但它同样可以应用于粘弹性流体，并且已经使得研究各种动力学问题成为可能，包括由Oldroyd-B本构方程描述的流体中囊泡的沉降和弹性细丝的游动。然而，迄今为止，关于该数值格式的精度或收敛性质的研究相对较少。在此，我们针对一个IB求解器应用于非平凡几何体内部和周围的粘弹性流动，使用理想化的Oldroyd-B以及更真实的、基于聚合物缠结的Rolie-Poly本构方程，给出了基准测试结果。我们使用二维数值测试算例以及流变学实验结果来对IB方法进行基准测试，并将其与更复杂的有限元和有限体积粘弹性流动求解器进行比较。此外，我们分析了正则化delta函数的不同选择以及相对拉格朗日网格间距，这使我们能够根据当前流动状态识别并推荐这些数值参数的关键选择。
英文摘要：
We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used for the simulation of biological fluid dynamics and other modeling scenarios where a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems with viscous incompressible fluids, it also can be applied to visoelastic fluids, and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constuitive equation. However, to date, relatively little work has explored the accuracy or convergence properties of the numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using the idealized Oldroyd-B and more realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime.
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