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.

中文翻译：

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沉浸式移动边界方案对离散元与晶格玻尔兹曼耦合方法的不稳定性及处理

浸入运动边界（IMB）方案已广泛用于将离散元素方法（DEM）与晶格玻尔兹曼方法（LBM）耦合。在文献中，仅给出了用于单固体颗粒覆盖的晶格结节细胞的IMB配方。很少讨论节点细胞被两个或多个固体颗粒覆盖的情况。已经发现，由于IMB公式中加权函数的计算不正确，在这种情况下可能会出现一些数值上的不稳定性。这项工作提出了一种增强的解决方案，可以解决问题并使用一些基准测试对其进行验证。此外，为了避免与治疗相关的额外费用并简化引入的复杂程序，提出了一种简化的IMB方案。增强和简化IMB方案的准确性均通过测试案例进行了验证，这些案例包括单粒子沉降，两粒子制图亲吻翻滚现象以及多粒子沉降。然后，使用经过特殊设计的气瓶通过测试来检验和讨论这两种方案的鲁棒性。事实证明，与增强型方案相比，简化的IMB方案更强大，更准确，更简单，更有效。