We propose a novel approach for two-way coupled simulations of multiphase flows within an Eulerian-Lagrange framework. Lagrangian particles are commonly approximated as point sources of either energy, mass or momentum. To introduce them into the Eulerian computation of the fluid flow, an approximation of the Dirac delta function has to be made. By resorting to the Boundary Element Method (BEM) based computation of fluid flow, it is possible to implement the point source concept without any numerical approximation by simply taking advantage of the properties of the fundamental solution present in BEM. However, singularity issues occur in the close vicinity of the mesh nodes. To remedy this effect, the particle-in-cell (PIC) method is used. We present a novel hybrid BEM-PIC two-way coupling algorithm and show that the proposed BEM-PIC model gives superior results compared to a standard PIC implementation. We introduce a critical distance to separate the domain, where the BEM model can be used and the domain, where the PIC model should be used. The results show that the BEM model can be used in about $97\%-99\%$ of the domain depending on the mesh used. We provide a criterion for estimating the critical distance within the novel hybrid BEM-PIC two-way coupling algorithm.

我们提出了一种新颖的方法，用于在欧拉-拉格朗日框架内进行多相流的双向耦合模拟。拉格朗日粒子通常被近似为能量，质量或动量的点源。为了将它们引入流体的欧拉计算中，必须对狄拉克δ函数进行近似。通过诉诸基于边界元方法（BEM）的流体流量计算，可以简单地利用BEM中存在的基本解的特性，而无需任何数值近似即可实现点源概念。但是，奇异性问题发生在网格节点的附近。为了补救此影响，使用了单元中粒子（PIC）方法。我们提出了一种新颖的混合BEM-PIC双向耦合算法，并表明与标准PIC实现相比，所提出的BEM-PIC模型给出了更好的结果。我们引入了一个临界距离，以分隔可使用BEM模型的域和应使用PIC模型的域。结果表明，BEM模型可用于约$97％-99％$域的大小取决于所使用的网格。我们提供了一种标准，用于估计新型BEM-PIC双向混合耦合算法中的临界距离。