“…Thus, the multiphase equations are inherently Eulerian in nature. Ruggirello et al [27] used the bulk material motion to formulate a multiphase Lagrangian method, but this requires the use of a drift velocity, such that the material is not constrained to the computational cell as in a standard single-phase Lagrangian method. The un-split method, also referred to as a direct-ALE method, reformulates the governing equations in a moving reference frame and solves the grid motion and fluid flow simultaneously in a single step [26,[28][29][30][31][32][33][34][35].…”