Abstract This paper describes a cell-based smoothed finite element method (CS-FEM) for computing unsteady viscoelastic fluid–structure interaction (VFSI) within the arbitrary Lagrangian–Eulerian framework. The incompressible Navier–Stokes equations incorporating the Oldroyd-B constitutive relation are decoupled via the smoothed characteristic-based split scheme that allows equal low-order interpolations for the triple primitive variables. The elastodynamics equation of a geometrically nonlinear solid is solved by the modified Newton–Raphson method in conjunction with the generalized- α method. Following an efficient moving mesh strategy, the block-Gauss–Seidel procedure is utilized to tightly couple three interacting fields. In particular, CS-FEM is adopted to spatially discretize the global VFSI system where all gradient related terms are readily smoothed. The cell-based smoothing concept is also introduced to evaluate viscoelastic fluid forces acting on the deformable body. Two transient VFSI examples are analyzed to demonstrate the enlarged applicability of CS-FEM. The main characteristics of viscoelastic flow-induced oscillations are successfully captured.

中文翻译：

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一种用于非定常粘弹性流固耦合的基于强耦合单元的平滑有限元求解器

摘要 本文描述了一种基于单元的平滑有限元方法 (CS-FEM)，用于在任意拉格朗日-欧拉框架内计算非定常粘弹性流固耦合 (VFSI)。包含 Oldroyd-B 本构关系的不可压缩 Navier-Stokes 方程通过基于平滑特征的拆分方案解耦，该方案允许对三元组原始变量进行相等的低阶插值。几何非线性固体的弹性动力学方程通过改进的 Newton-Raphson 方法结合广义α 方法求解。遵循有效的移动网格策略，块-高斯-赛德尔过程用于紧密耦合三个相互作用的场。特别是，CS-FEM 用于空间离散全局 VFSI 系统，其中所有与梯度相关的项都很容易平滑。还引入了基于单元的平滑概念来评估作用在可变形体上的粘弹性流体力。分析了两个瞬态 VFSI 示例，以证明 CS-FEM 的扩大适用性。粘弹性流动引起的振荡的主要特征被成功捕​​获。