Compressible multiphase particle-in-cell method (CMP-PIC) for full pattern flows of gas-particle system

•A novel particle flow model combining the merits of MP-PIC, DEM and two-fluid BN model.•Accurate collision resolving by a coarse-grained DEM with no empirical parameters.•Consistent discretization scheme for flux and nozzling terms to suppress numerical oscillation.•High-order interpolation operator to achieve high-accuracy and robust simulation.•Verification tests including full pattern compressible particle flows show reliability and validity of CMP-PIC. The compressible multiphase flows in a gas-particle system often arise in many engineering applications and nature phenomena. This study focuses on the development of a novel method, i.e. the compressible multiphase particle-in-cell (CMP-PIC), which can be capable of simulating all pattern flows of gas-particle system from dilute to dense and granular flows. The equivalent relation of the momentum equations of the particle phase between the Baer and Nunziato (B-N) model and the MP-PIC model is the key support for the modeling of gas phase, particle phase and coupling effects. For the gas phase, the governing equations are constructed in the Eulerian frame and the B-N model is taken as reference to derive the equations of gas phase and two-way coupling terms. A transport five-equation model for multi-material compressible flows is adopted in gas equation. Additionally, the disperse particle is tracked in the Lagrangian coordinate based on the particle-in-cell (PIC) method. The collisions among particles are simulated with coarse-grained discrete element method (DEM) model which provides more physical manner rather than empirical collision stress model. Moreover, a two-way coupling model is derived based on a comparative study with B-N model. Thereafter a set of unified HLL/HLLC solvers is developed for the discretization of the convective and nozzling terms of gas phase equations. A high order interpolation operator with certain enlarged smooth length is applied for the robust computation of coupling effects. Overall, the advantages of traditional compressible two-fluid model, DEM and PIC model are integrated into the current CMP-PIC model, and it can simulate the transition flows from dilute to dense or vice versa, which is difficult for traditional methods. This Eulerian-Lagrangian approach is implemented in an in-house parallel code and validated against experimental observations involving different shock induced multiple phase flows. The qualitative and quantitative comparison shows that numerical re