A combined immersed boundary and discrete unified gas kinetic scheme for particle–fluid flows

Abstract

A discrete unified gas kinetic scheme (DUGKS) coupled with the immersed boundary (IB) method is developed to perform interface-resolved simulation of particle-laden flows. The present method (IB-DUGKS) preserves the respective advantages of the IB and DUGKS, i.e., the flexibility and efficiency for treating complex flows, and the robustness and low numerical-dissipation. In IB-DUGKS, the IB method is used to treat the fluid–solid interfaces and the DUGKS is applied to simulate the fluid flow, making use of the Lagrangian and Eulerian meshes, respectively. Those two meshes are fully independent, which contributes to the avoidance of grid regeneration when a solid particle moves. Specifically, in the present implementation of IB-DUGKS, the no-slip boundary condition at the particle surface is accurately enforced by introducing an efficient iterative forcing algorithm, and the IB force induced by the particle boundary is conveniently incorporated into the DUGKS with the Strang–Splitting scheme. The accuracy of the IB-DUGKS is first verified in the flows past a stationary cylinder and an oscillating cylinder in a quiescent fluid. After that, several well-established two- and three-dimensional particulate flow problems are simulated, including the sedimentation of a particle and the DKT dynamics of two particles in a channel, and a group of particles settling in an enclosure. In all test cases, the results are in good agreement with the data available in the literature, demonstrating that the proposed IB-DUGKS is a promising tool for simulating particulate flows.