论文标题
凯奇方法的重构：一种用于流体厚结构相互作用问题的二阶分区方法
Refactorization of Cauchy's method: a second-order partitioned method for fluid-thick structure interaction problems
论文作者
论文摘要
这项工作着重于用于流体结构相互作用问题的新型，强耦合分区方法的推导和分析。假定该流量是粘性和不可压缩的，并且结构是使用线性弹性动力学方程进行建模的。我们假设结构是厚的，即使用与流体相同数量的空间尺寸进行建模。我们新开发的数值方法基于广义的罗宾边界条件，以及Cauchy单足类的“ Theta Like”方法的重构，作为一系列向后的Euler-Forwhard Euler步骤，用于分散该问题。对于[0.5,1]中的任何theta而言，该方法均为theta参数，对于theta = 0.5+o（tau），tau是时间步长的二阶精度。在拟议的算法中，使用向后的Euler方案离散的流体和结构子问题首先迭代求解直至收敛。然后，变量是线性的，相当于解决前向欧拉问题。我们证明迭代过程是收敛的，并且提出的方法在[0.5,1]中提供了稳定的theta。基于空间中有限元离散化的数值示例，使用问题中的参数值不同，并将我们的方法与文献中的其他强耦合分区方案进行比较。我们还将我们的方法与基准问题的单片和非题分配的求解器进行比较，并在血流的生理范围内进行参数，与单片方案达到了极好的一致性。
This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear elastodynamics equations. We assume that the structure is thick, i.e., modeled using the same number of spatial dimensions as fluid. Our newly developed numerical method is based on generalized Robin boundary conditions, as well as on the refactorization of the Cauchy's one-legged `theta-like' method, written as a sequence of Backward Euler-Forward Euler steps used to discretize the problem in time. This family of methods, parametrized by theta, is B-stable for any theta in [0.5,1] and second-order accurate for theta=0.5+O(tau), where tau is the time step. In the proposed algorithm, the fluid and structure subproblems, discretized using the Backward Euler scheme, are first solved iteratively until convergence. Then, the variables are linearly extrapolated, equivalent to solving Forward Euler problems. We prove that the iterative procedure is convergent, and that the proposed method is stable provided theta in [0.5,1]. Numerical examples, based on the finite element discretization in space, explore convergence rates using different values of parameters in the problem, and compare our method to other strongly-coupled partitioned schemes from the literature. We also compare our method to both a monolithic and a non-iterative partitioned solver on a benchmark problem with parameters within the physiological range of blood flow, obtaining an excellent agreement with the monolithic scheme.
