Numerical method for compressible gas-particle flow coupling using adaptive parcel refinement (APR) method on non-uniform mesh

The Eulerian–Lagrangian (EL) approach is usually used for simulating the compressible gas-particle flows. In our previous study, we have developed the compressible multiphase particle-in-cell method (CMP-PIC) and achieved good results for both dilute and dense compressible gas-particle flow. However, the original CMP-PIC was only implemented on the uniform mesh, which limits its resolution, efficiency, and application in the field of engineering. Therefore, in the present study, we have implemented the developed algorithms for coupling terms and the adaptive parcel refinement APR method on the non-uniform mesh. The algorithm of coupling terms is a new method for interpolating between a parcel with definite volume and cells with different volumes; this has not been investigated in previous particle-in-cell (PIC) research. The improved operator of the multiphase coupling terms is put forward to adapt the wide range size ratios since directly using the original operator causes the loss of coupling effects. The APR sets up a numerical “breakup model” of a parcel from the computational perspective, which represents a new approach to a parcel-type numerical method. In the APR method, the parcel resolution can automatically match the resolution of the local Eulerian cell. Therefore, the improved CMP-PIC can handle the simulation when a large parcel enters the fine cell and prevents the abnormal termination due to non-physical packing of particles. Based on conservation and scaling laws, the strategy, split criterion, and split configuration are identified to correlate the parameters of the parent and child parcels. Additionally, the algorithms of the multiphase HLL/HLLC solvers are derived for flux and nozzling terms to adapt the Cartesian grid with varying cell sizes, which is a type of non-uniformity. Several one-dimensional and two-dimensional tests show the correctness and advantages of using the non-uniform mesh, improved operator, and APR method. Results show that the combination of improved interpolation operator and APR method can significantly improve the reliability, resolution of simulation results, and robustness of the algorithm. The simulation time is also reduced due to regional refinement.