An improved predictive-corrective incompressible smoothed particle hydrodynamics method for fluid flow modelling

Predictive-corrective incompressible smoothed particle hydrodynamics (PCISPH) is an efficient SPH variation originally developed for computer graphics. Its application in modeling physics-focused fluid flows has not yet been reported. In this work, an improved PCISPH method is presented for physics-focused fluid flow modeling. Different from traditional weakly-compressible SPH (WCSPH) and incompressible SPH (ISPH), PCISPH satisfies the incompressibility requirement at the particle level without a predefined equation of state. The pressure is obtained using an iterative predictive-corrective scheme at each individual particle. The presented PCISPH allows much larger time steps compared with WCSPH. It also avoids the time-consuming solution of Pressure Poisson Equation (PPE) in ISPH. Consequently, the PCISPH has high computational efficiency even with millions of computational particles. To ensure physically correct modeling of fluid flows, we employ several techniques to enhance the accuracy and stability of the PCISPH: (1) the continuity equation is used to predict density, replacing the mass summation approach used in the original PCISPH, (2) numerical diffusion and pressure smoothing are introduced to improve the pressure computation, (3) a generalized boundary treatment approach which can handle arbitrarily complex geometries is employed, (4) an adaptive time-stepping algorithm is used, allowing efficient simulation as well as ensuring stability. The performance of the improved PCISPH is systematically investigated using three standard SPH validation cases. Comparisons between the improved PCISPH and the state-of-the-art δ — SPH are presented. It is found that the improved PCISPH gives numerical results as accurate as δ — SPH, except for having moderate temporal pressure oscillations. However, the numerical results show that the improved PCISPH is approximately five times faster than δ — SPH. The improved PCISPH method shows to be a promising tool for large-scale three-dimensional fluid flow modeling.