Instability and treatments of the coupled discrete element and lattice Boltzmann method by the immersed moving boundary scheme

The immersed moving boundary (IMB) scheme has been extensively used to couple the discrete element method (DEM) with the lattice Boltzmann method (LBM). In the literature, only the formulation of IMB for lattice nodal cells covered by a single-solid particle was given. The treatment of situations where a nodal cell is covered by two or more solid particles is seldom discussed. It is found that some numerical instability can occur for such situations due to an inappropriate computation of the weighting function in the IMB formulation. This work presents an enhanced treatment that can resolve the issue and validates it using some benchmark tests. Furthermore, to avoid the extra costs associated with the treatment and simplify the complicated procedure introduced, a simplified IMB scheme is proposed. The accuracy of both enhanced and simplified IMB schemes are validated by test cases including single-particle sedimentation, two-particle drafting-kissing-tumbling phenomenon, and multiple-particle sedimentation. Then, the robustness of both schemes is examined and discussed using a specially designed flow past cylinders test. The simplified IMB scheme is proved to be robust and sufficiently accurate and simpler and more effective than the enhanced scheme.