Eulerian-Lagrangian and Eulerian-Eulerian approaches for the simulation of particle-laden free surface flows using the lattice Boltzmann method

This paper studies the Eulerian-Lagrangian and Eulerian-Eulerian approaches for the simulation of interaction between free surface flow and particles. The dynamics of the fluid as well as the transport of the particles in the Eulerian description is solved using the lattice Boltzmann method. To minimize artificial diffusion in particle transport the lattice Boltzmann method with direction-dependent stabilization is proposed. The interaction between the fluid and particles is ensured using the particulate immersed boundary method, where the two-ways coupling algorithm is considered. The developed Eulerian-Lagrangian and Eulerian-Eulerian schemes are compared with each other and validated against results from literature. Both schemes are applied to free surfaces flow problems with complex geometries similar to real gravity casting problems with fillers