MPS-WCMPS coupled method for bubble dynamic with density and pressure discontinuity

Wang, Z. ; 杉山 智之 

Wang, Z.; Sugiyama, Tomoyuki

Bubble dynamics are commonly encountered in a wide range of engineering applications. However, abrupt density and pressure drop would occur at the interface due to the discontinuity of fluid properties, e.g., density, viscosity and surface tension. Owing to the mathematical discontinuity, numerical simulation of bubble dynamic, especially for large density ratio, is always challenging. The Lagrangian particle methods, such as the Moving Particle Semi-implicit method (MPS), have attracted great attentions in simulating free surface and multiphase flows due to its distinct advantage in tracking moving interfaces. This study presents a new coupled particle method for bubble dynamic with large density ratio. The proposed scheme couples the incompressible MPS and Weakly Compressible MPS, representing the liquid and gas phases, respectively. The liquid-gas phase interface is explicitly represented by a moving interface mesh, consisting of discrete nodes. The stress balance equations at the interface are adequately enforced on these interface nodes. The surface tension is considered as a pressure jump at the interface rather than treated as volume force. Without applying the smoothing or averaging scheme, the density and viscosity are preserved discontinuous across the interface. Benefiting from the least squares scheme, axisymmetric formulation is straightforwardly introduced. To save computational cost, a multi-time step algorithm is developed further. Moreover, to maintain quasi-irregular particle distribution and control the multi-spatial resolution dynamically, a user-defined particle shifting scheme is proposed. Several benchmark tests are conducted to verify the accuracy and efficiency of the developed method. Satisfying agreements are obtained by comparing with reported numerical solutions and experimental data.