Fictitious boundary and moving mesh methods for the numerical simulation of rigid particulate flows

In this paper, we investigate the numerical simulation of rigid particulate flows using a new moving mesh method combined with the multigrid fictitious boundary method (FBM) [9, 10]. With this approach, the mesh is dynamically relocated through a special partial differential equation to capture the region near the surface of the moving particles with high accuracy. The complete system is realized by solving the mesh movement and physical partial differential equations alternately. The flow is computed by an ALE formulation with a multigrid finite element solver, and the solid particles are allowed to move freely through the computational mesh which is adaptively aligned by the moving mesh method based on an arbitrary grid. The important aspect is that the data structures of the underlying undeformed mesh, in many cases a tensorproduct mesh, are preserved while only the spacing between the grid points is adapted in each step. Numerical results demonstrate that the interaction between the fluid and the particles can be accurately and efficiently handled by the presented method. It is also shown that the presented method directly improves upon the previous pure multigrid FBM to solve particulate flows with many moving rigid particles.