论文标题
用于流体与厚结构之间相互作用的非题性域分解方法
A non-iterative domain decomposition method for the interaction between a fluid and a thick structure
论文作者
论文摘要
这项工作着重于对移动域，流体结构相互作用问题的分区数值方法的开发和分析。我们使用不可压缩的Navier-Stokes方程和使用线性弹性方程式对流体进行建模。我们假设结构厚，即与流体相同的维度描述。我们提出了一种非著作，域分解方法，其中流体和结构子问题分别解决。该方法基于广义的罗宾边界条件，这些条件均用于流体和结构子问题。使用能量估计，我们表明应用于移动域问题的提出方法无条件稳定。我们还分析了该方法的收敛性，并显示$ \ MATHCAL {O}（ΔT^\ frac12）$在时间上的收敛性和最佳收敛。数值示例用于证明该方法的性能。特别是，我们探讨了在广义罗宾边界条件的推导中使用的组合参数与方案准确性之间的关系。我们还将方法的性能与整体求解器进行了比较。
This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear elasticity equations. We assume that the structure is thick, i.e., described in the same dimension as the fluid. We propose a non-iterative, domain decomposition method where the fluid and the structure sub-problems are solved separately. The method is based on generalized Robin boundary conditions, which are used in both fluid and structure sub-problems. Using energy estimates, we show that the proposed method applied to a moving domain problem is unconditionally stable. We also analyze the convergence of the method and show $\mathcal{O}(Δt^\frac12)$ convergence in time and optimal convergence in space. Numerical examples are used to demonstrate the performance of the method. In particular, we explore the relation between the combination parameter used in the derivation of the generalized Robin boundary conditions and the accuracy of the scheme. We also compare the performance of the method to a monolithic solver.
