An immersed interface-lattice Boltzmann method (II-LBM) is developed for modeling fluid-structure systems. The key element of this approach is the determination of the jump conditions that are satisfied by the distribution functions within the framework of the lattice Boltzmann method where forces are imposed along a surface immersed in an incompressible fluid. In this initial II-LBM, the discontinuity related to the normal component of the interfacial force is sharply resolved by imposing the relevant jump conditions using an approach that is analogous to imposing the corresponding pressure discontinuity in the incompressible Navier-Stokes equations. We show that the jump conditions for the distribution functions are the same in both single-relaxation-time and multi-relaxation-time LBM formulations. Tangential forces are treated using the immersed boundary-lattice Boltzmann method (IB-LBM). In our implementation, a level set approach is used to impose jump conditions for rigid-body models. For flexible boundary models, we describe the moving interface by interpolating the positions of marker points that move with the fluid. The II-LBM introduced herein is compared to a direct forcing IB-LBM for rigid-body fluid-structure interaction, and a classical IB-LBM for cases involving elastic interfaces. Higher order accuracy is observed with the II-LBM as compared to the IB-LBM for selected benchmark problems. Although our II-LBM only imposes jump conditions corresponding to the pressure, the error in the velocity field is demonstrated to be much smaller for the II-LBM than the IB-LBM. The II-LBM is also demonstrated to provide superior volume conservation when simulating flexible boundaries.

开发了一种用于对流体结构系统进行建模的沉浸式界面格子Boltzmann方法（II-LBM）。这种方法的关键要素是确定由跳变条件确定的跳变条件，该跳变条件是在格子Boltzmann方法的框架内进行的，其中力沿着浸入不可压缩流体中的表面施加力。在此初始II-LBM中，通过使用类似于在不可压缩的Navier-Stokes方程中施加相应压力不连续性的方法来施加相关的跳跃条件，可以急剧地解决与界面力的法向分量有关的不连续性。我们表明，在单弛豫时间和多弛豫时间的LBM公式中，分布函数的跳跃条件都相同。切向力使用浸没边界格子玻尔兹曼方法（IB-LBM）进行处理。在我们的实现中，使用水平集方法为刚体模型施加跳跃条件。对于灵活的边界模型，我们通过内插随流体移动的标记点的位置来描述移动界面。将本文介绍的II-LBM与用于刚体流体-结构相互作用的直接强迫IB-LBM和用于涉及弹性界面的经典IB-LBM进行了比较。对于选定的基准问题，与IB-LBM相比，使用II-LBM观察到了更高的定单精度。尽管我们的II-LBM仅施加了与压力相对应的跳跃条件，但事实证明，对于II-LBM，速度场中的误差要比IB-LBM小得多。