Fluid-structure interaction (FSI) problems with strong nonlinearity and multidisciplinarity pose challenges for current numerical FSI algorithms. This work proposes a monolithic strategy for solving the equations of motion for both the fluid and structural domains under the unique Lagrangian framework of the B-spline material point method (BSMPM). A node-based density smoothing BSMPM (referred to as ds-BSMPM) is proposed to eliminate pressure instability and oscillation in the simulation of weakly compressible fluids, which is straightforwardly implemented using B-spline basis functions without the need for any sophisticated particle search algorithm. The interaction between the fluid and structure is conducted using the Lagrangian multiplier method on the tensor product grid, whose actual position is determined by the Greville abscissa and is used to detect contact. The proposed method is verified and validated against existing numerical approaches and experimental results, demonstrating the effectiveness of the proposed method in eliminating the oscillations of water pressure and solid stress, and avoiding premature and erroneous contact. In particular, this work presents a promising monolithic approach for achieving high-fidelity solutions to complex FSI problems.

中文翻译：

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使用密度平滑 B 样条材料点法和接触方法模拟流固耦合


具有强非线性和多学科性的流固耦合 （FSI） 问题对当前的数值 FSI 算法提出了挑战。这项工作提出了一种整体策略，用于在 B 样条材料点法 （BSMPM） 的独特拉格朗日框架下求解流体域和结构域的运动方程。提出了一种基于节点的密度平滑 BSPM（称为 ds-BSMPM）来消除弱可压缩流体模拟中的压力不稳定和振荡，这是使用 B 样条基函数直接实现的，不需要任何复杂的粒子搜索算法。流体和结构之间的相互作用是在张量积网格上使用拉格朗日乘子方法进行的，其实际位置由 Greville 横坐标确定，用于检测接触。结合现有的数值方法和实验结果，验证了所提方法的有效性，证明了所提方法在消除水压和固体应力振荡、避免过早和错误接触方面的有效性。特别是，这项工作提出了一种很有前途的单体方法，用于实现复杂 FSI 问题的高保真解决方案。