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.

本文研究了用于模拟自由表面流动和粒子之间相互作用的欧拉-拉格朗日和欧拉-欧拉方法。欧拉描述中的流体动力学以及粒子的传输是使用格子玻尔兹曼方法求解的。为了最大限度地减少粒子传输中的人工扩散，提出了具有方向相关稳定性的晶格玻尔兹曼方法。流体和粒子之间的相互作用是使用颗粒浸入边界方法来保证的，其中考虑了双向耦合算法。将开发的欧拉-拉格朗日和欧拉-欧拉方案相互比较，并根据文献结果进行验证。