To solve the solid–fluid interaction with Navier–slip boundary condition, we propose a new method in this paper. In this approach, the solid body is modeled by the Newton’s equations and the fluid is assumed to satisfy the discrete lattice Boltzmann equations. The Navier–slip boundary condition is applied as the velocity boundary condition for the solid–fluid interface. We discretize the Newton’s equations by a prediction/correction approach and the discrete lattice Boltzmann equations by a second–order finite difference scheme in space together with a second–order Range–Kutta scheme in time. The Navier–slip boundary condition and the immersed boundary body force are almost implicitly updated by using the implicit velocity correction–based immersed boundary–lattice Boltzmann method. Numerical simulations are carried out to verify the new presented method.

为了解决Navier-滑移边界条件下的固液相互作用，我们提出了一种新的方法。在这种方法中，通过牛顿方程对实体进行建模，并假设流体满足离散晶格玻尔兹曼方程。Navier-滑移边界条件被用作固-液界面的速度边界条件。我们通过预测/校正方法离散牛顿方程，并通过空间上的二阶有限差分方案以及时间上的二阶Range-Kutta方案离散离散格子Boltzmann方程。Navier-滑移边界条件和沉浸边界体力几乎是通过使用基于隐式速度校正的沉浸边界网格Boltzmann方法隐含更新的。