This work presents an arbitrary Lagrangian Eulerian (ALE) method for the compressible two-phase flow ejecta transporting model with the HLLC-2D Riemann solver. We focus on researching the precise equation to describe the interactions between particle phase and flow phase. The calculation of the momentum and energy exchange across two phases is the key point during the procedure, which can be capable of maintaining the conservation of this system. For particles, tracking their trajectories within the mesh and elements is essential. Thereafter an ALE method instead of Lagrangian scheme is derived for the discretization of the equation to perform better with the complex motion of particles and flow. We apply the HLLC-2D Riemann solver to substitute the HLLC solver which relaxes the limitation for continuous fluxes along the edge. Meanwhile we propose a method for searching particles and provide a CFL-like condition based on this. Finally, we show some numerical tests to analysis the influence of particles on fluid and get a following effect between two phases. The model and the numerical method are validated through numerical tests to show its robustness and accuracy.

翻译：本文提出了一种采用HLLC-2D黎曼求解器的可压缩两相流抛射物输运模型的任意拉格朗日-欧拉（ALE）方法。我们重点研究了描述颗粒相与流体相相互作用的精确方程。两相间动量与能量交换的计算是过程中的关键环节，该方法能够保持系统的守恒性。对于颗粒而言，追踪其在网格与单元内的运动轨迹至关重要。为此，我们推导了采用ALE方法（而非拉格朗日格式）的方程离散化方案，以更好地处理颗粒与流体的复杂运动。我们采用HLLC-2D黎曼求解器替代HLLC求解器，从而放宽了沿单元边界通量连续性的限制。同时，我们提出了一种颗粒搜索方法，并据此给出了类CFL条件。最后，我们通过若干数值算例分析了颗粒对流体的影响，并观测到两相间的跟随效应。数值试验验证了该模型与数值方法的鲁棒性与精确性。