An axisymmetric multiphase SPH model for the simulation of rising bubble

3-D SPH simulations are often time-consuming due to the massive particle numbers. For the problem which has axisymmetric characteristics, the solving of the entire three-dimensional domain can be simplified which saves computational cost dramatically. In this paper, a novel derivation for the SPH formulation in cylindrical coordinate is presented, which is straightforward and physically meaningful. A multiphase numerical model is developed based on the derived formulation including the discretization formulas of surface tension force, viscous force, interface sharpness force and the treatment of high density ratio near the multiphase interface, as well as an improved anti-penetration treatment close to the axis. The effectiveness and robustness of the proposed multiphase SPH model are demonstrated via the classical surface-tension test and bubble rising problems at different conditions. The results are compared with analytical solutions, the experimental data and other numerical results. The promising results of the novel axisymmetric SPH model demonstrate a great potential for an efficient SPH modeling of complex axisymmetric multiphase flows. Dramatic efficiency boost is achieved by comparing the axisymmetric simulation with 3-D simulation in terms of CPU time. •This article is dedicated to the improvement of SPH in cylindrical coordinate.•A novel derivation of axisymmetric SPH formulation is presented.•A multiphase model based on axisymmetric SPH is developed.•The newly proposed axisymmetric SPH formulas can simulate fully developed multiphase flows.•Large efficiency boost is observed when comparing with purely 3-D simulations.