An improved Multiphase Moving Particle Semi-implicit method in bubble rising simulations with large density ratios

In this study, an improved MMPS-CA method is developed against the inaccuracy of MMPS-CA (Continuous Acceleration) method in simulating bubble rising cases with large density ratios. A higher order Laplacian model is adopted to discretize pressure Poisson equation and a ECS source term with compressible form is adopted. A new multi-viscosity model is developed based on the Shepherd smoothing function, and the performances of different multi-viscosity models in bubble rising cases are investigated in detail. A higher order accuracy density smoothing scheme base on the Gaussian function is employed to avoid the unphysical invasions through the interface, and a dynamic displacement modification technique is developed to make the particle distribution more uniform in the calculation. Then several multiphase simulation cases including the stratified pool case, deformation of 2D square droplet case, single bubble rising case, two-phase Poiseuille flow case and the bubble rising benchmark case are employed to verify the robustness of the improved MMPS-CA method. Bubble pairs rising and coalescence cases are carried out to further verify the ability of the proposed method in simulating bubbles' behaviors. Results of the improved MMPS method fit well enough to other numerical and experimental results. At the end of the paper, a 2D closed air-water separator case is carried out to investigate the robustness of the improved MMPS-CA method in general bubble rising simulations with large density ratios.