Abstract A two-way coupling method of the three-dimensional (3D) isogeometric approach and the least-square moving particle semi-implicit method (LSMPS) is presented for handling the fluid–structure interaction problems. This method takes advantages of isogeometric analysis (IGA) for structure deformation, e.g. the exact representation of the structure geometry and high accuracy for solution fields with relatively few elements, and that of the LSMPS method for fluid flow, e.g. its consistent discretization for both internal particles and boundary conditions. When the fluid is solved by the LSMPS method, the NURBS (Non-Uniform Rational B-Splines) surfaces provide boundary conditions for the LSMPS method. Afterward, the pressure on the NURBS surface is first evaluated from the pressure and the corresponding derivatives at the LSMPS particles by using the Taylor series expansion, and then integrated to determine the pressure force at the virtual points on the NURBS surface by using the Newton–Cotes method. Subsequently, the pressure forces at the virtual points are distributed onto the control nodes (i.e. control points) of the IGA elements so that the structure deformation can be analyzed by using the IGA method. The coupling algorithm is based on a Lagrangian framework and can handle the boundary conditions and the fluid–structure interactions accurately and easily. Finally, three examples, i.e. fluid flowing in a rigid pipe, fluid-tank, and fluid-torus interactions in the elastic regime, are simulated to demonstrate the accuracy and validity of the proposed coupling method.

中文翻译：

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用于模拟流固耦合的耦合 3D 等几何/最小二乘 MPS 方法

摘要 提出了一种三维（3D）等几何方法和最小二乘移动粒子半隐式方法（LSMPS）的双向耦合方法来处理流固耦合问题。这种方法利用了结构变形的等几何分析（IGA）的优点，例如结构几何的精确表示和具有相对较少元素的解场的高精度，以及流体流动的 LSMPS 方法，例如它对内部结构的一致离散化粒子和边界条件。当使用 LSMPS 方法求解流体时，NURBS（非均匀有理 B 样条）曲面为 LSMPS 方法提供边界条件。之后，NURBS 表面上的压力首先通过使用泰勒级数展开从 LSMPS 粒子处的压力和相应的导数进行评估，然后使用 Newton-Cotes 方法积分以确定 NURBS 表面上虚拟点处的压力. 随后，将虚拟点处的压力分布到IGA 单元的控制节点（即控制点）上，从而可以使用IGA 方法分析结构变形。耦合算法基于拉格朗日框架，可以准确、轻松地处理边界条件和流固耦合。最后，三个例子，即流体在刚性管道中流动，流体罐，以及在弹性状态下的流体环面相互作用，