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

Abstract

In this paper, we investigate the numerical simulation of particulate flows using a new moving mesh method combined with the multigrid fictitious boundary method (FBM) [S. Turek, D.C. Wan, L.S. Rivkind, The fictitious boundary method for the implicit treatment of Dirichlet boundary conditions with applications to incompressible flow simulations. Challenges in Scientific Computing, Lecture Notes in Computational Science and Engineering, vol. 35, Springer, Berlin, 2003, pp. 37–68; D.C. Wan, S. Turek, L.S. Rivkind, An efficient multigrid FEM solution technique for incompressible flow with moving rigid bodies. Numerical Mathematics and Advanced Applications, ENUMATH 2003, Springer, Berlin, 2004, pp. 844–853; D.C. Wan, S. Turek, Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method, Int. J. Numer. Method Fluids 51 (2006) 531–566]. With this approach, the mesh is dynamically relocated through a (linear) partial differential equation to capture the surface of the moving particles with a relatively small number of grid points. The complete system is realized by solving the mesh movement and the partial differential equations of the flow problem alternately via an operator-splitting approach. The flow is computed by a special 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 in every time step. One important aspect is that the data structure of the undeformed initial mesh, in many cases a tensor-product mesh or a semi-structured grid consisting of many tensor-product meshes, is preserved, while only the spacing between the grid points is adapted in each time step so that the high efficiency of structured meshes can be exploited. 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 significantly improves the accuracy of the previous multigrid FBM to simulate particulate flows with many moving rigid particles.