  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.
