A sharp-interface immersed-boundary method that does not smear the boundaries, is easy to implement, and is straightforward in handling the Neumann condition as compared to previous methods is developed for compressible flows to simulate the interaction of solid particles with shocks. The inviscid and viscous fluxes of compressible flow equations in curvilinear coordinates are discretized with a third-order weighted essentially nonoscillatory (WENO) scheme and a central scheme, respectively. The equations are advanced in time using a third-order Runge–Kutta method. The sharp interface at the immersed boundaries is maintained by reconstructing the flow variables along the normal direction to the boundary. The WENO discretization is reverted to a biased essentially nonoscillatory scheme near the immersed boundaries to avoid using the nodes that are inside the immersed boundary. The method is validated against experimental measurements and shown to be between second- and third-order-accurate in the presence of immersed boundaries. The method is applied to simulate shock-tube experiments involving the interaction of a moving normal shock with a stationary cylinder as well as a cylindrical and a spherical particle accelerating by a shock. The numerical results capture all of the shock features observed in the experiments and show great agreement with the measurements and previous benchmark solutions. The results show that the acceleration of a sphere due to an incident shock highly depends on the density ratio of the sphere to the incoming fluid.

与以前的方法相比，针对可压缩流开发了一种尖锐的界面浸入边界方法，该方法不涂抹边界，易于实施，并且在处理诺伊曼条件时非常简单，可模拟固体颗粒与冲击的相互作用。曲线坐标中可压缩流动方程的无粘性和粘性通量分别通过三阶加权基本非振荡（WENO）方案和中央方案离散化。使用三阶Runge–Kutta方法可在时间上推进方程。通过沿着边界的法线方向重构流量变量，可以保持在浸入边界处的尖锐界面。WENO离散化在沉浸边界附近恢复为有偏的基本非振荡方案，以避免使用沉浸边界内部的节点。该方法针对实验测量进行了验证，并且在存在浸入边界的情况下显示在二阶和三阶精度之间。该方法用于模拟激波管实验，该实验涉及运动的法向激波与固定圆柱体以及通过激波加速的圆柱和球形粒子之间的相互作用。数值结果记录了实验中观察到的所有冲击特征，并与测量结果和以前的基准解决方案非常吻合。结果表明，由于入射冲击而引起的球体加速度很大程度上取决于球体与传入流体的密度比。