Enhancement of stability of 3D moving particle semi-implicit method by artificial viscosity

By the virtue of Lagrangian gridless particle method, the moving particle semi-implicit (MPS) method has been applied in a wide range of engineering applications. However, the built-in instability in computational algorithm has seriously limited its further development and application. In this paper, aiming at developing 3D stabilized MPS method, a comprehensive comparison of stabilizing methods proposed by different researchers has been conducted, in which many elements leading to instability are considered. Then the equations proposed in 2D are extended to 3D and an artificial viscosity model based on smooth particle hydrodynamics (SPH) is proposed to reduce instability in MPS for the first time. With the different combinations of proposed methods and models, the deforming process of a swirling cubic fluid patch and hydrostatic pressure problem are simulated comparatively. The results are also compared with those from volume of fluid (VOF) model conducted by a commercial software. The accuracy and stability of proposed methods and models are validated. It is concluded that: for 3D case, only extending and applying previous stabilizing method is still dissatisfactory, while good effects in accuracy and stability can be obtained by incorporating the artificial viscosity model proposed in present paper. And it is also revealed that no negative effects on exactness of pressure solution will be produced, and thus on the flow field.