In this paper, a wavelet immersed boundary (IB) method is proposed to solve fluid-structure interaction (FSI) problems with two-variable coupling, in which it is an interaction between fluid force and boundary deformation. This wavelet IB method is developed by introducing a wavelet finite element method to calculate the FSI force affected by the two-variable coupling. Furthermore, a boundary influence matrix and a series of B-spline wavelet delta functions are constructed to restrain the non-physical force oscillations. Finally, several FSI problems are simulated, which include flows past a fixed circular cylinder and a crosswise oscillating circular cylinder, as well as an in-line oscillating circular cylinder in a rest fluid. The numerical examples show that the new method is a simple and efficient method for two-variable coupled FSI problems.

本文提出了一种小波浸入边界（IB）方法来解决两变量耦合的流固耦合问题，即流体力与边界变形之间的相互作用。该小波IB方法是通过引入小波有限元方法来计算受两变量耦合影响的FSI力而开发的。此外，构造边界影响矩阵和一系列B样条小波三角函数以约束非物理力的振荡。最终，模拟了几个FSI问题，包括流过固定的圆柱体和横向振荡的圆柱体以及静止流体中的直列振荡的圆柱体的流量。数值算例表明，该新方法是解决两变量耦合FSI问题的一种简单有效的方法。