Simulation of interaction between shocks and particle cloud using a second-order conservative sharp interface method

Abstract

In this paper we present a second-order accurate conservative sharp interface method capable of simulating displacements and collisions of many particles in compressible inviscid flows. We implement a cut cell algorithm to resolve moving particles of arbitrary shape on a Cartesian mesh, thereby generating unstructured body-fitted meshes near the particle surfaces and structured meshes away from the particles. A second-order finite volume method in the arbitrary Lagrange-Eulerian framework is used for the discretization of the Euler equations, so that exact conservation of mass, momentum and energy is enforced for the flow computations, even in the presence of moving particles. The boundary condition at the particle surfaces is enforced by solving a local Riemann problem, which is constructed in the direction normal to the solid surface. The movement of a particle is affected by the forces exerted by the surrounding fluid and its collisions with other particles. A hard sphere model is proposed to deal with the particle collisions; in particular, it is capable of handling multi-body collisions occurring in no-dilute particle clouds, regardless of the number of particles involved. Furthermore, the model ensures the conservation of momentum and energy during the collision process. The method is validated by comparing against benchmark solutions or experimental data available in the literature, for test cases such as supersonic flows past a stationary cylinder and lift-off of rigid cylinders after shock impact. Good agreement has been achieved qualitatively and quantitatively. The method is also used to investigate the complicated flow phenomena, e.g. transport of particle clouds in supersonic flows through a confined channel and the interaction between shocks and three-dimensional particles.