Sharp-Interface Immersed-Boundary Method for Compressible Flows with Shock–Particle Interaction

Abstract

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.