Research On Weakly-compressible SPH And Godunov-type SPH Methodology For Multiphase Fluid

Multiphase flows are common and important phenomenon in the field of ship and ocean engineering. Dynamic tracking of the interfaces between different phases is one of the key issues in multiphase simulations. As a meshfree Lagrangian method, the interface between different flows can be naturally formed in Smoothed Particle Hydrodynamics (SPH) method. Which gives it tremendous advantages in modeling multiphase flows. In this paper, we focus on further developing multiphase SPH algorithms and their applications in ship and ocean engineering.The weakly-compressible SPH (WCSPH) gives an explicit solution for incompressible flows. However, the standard single-phase WCSPH is not suitable for multiphase flows because of the numerical instability caused by the discontinuities of density and pressure gradient over the interface. Various multiphase SPH models have been proposed in order to solve this problem. In this present work, focusing on the flaws in existing multiphase SPH models, we propose an interfacial pressure correction algorithm to eliminate the unphysical pressure propagation over the interface. Four numerical examples of air-water flows, including still water test, sloshing, dam breaking and water entry, are presented and compared with analytical results or experimental data. It turns out that the correction algorithm greatly improves the numerical stability in long-term simulations, and is also able to achieve good results in short-term problems. In addition, the analysis of the tensile stability is conducted on the improved multiphase SPH model, which shows that the correction algorithm does not lower the overall stability criteria. Two more numerical examples are presented to validate the tensile stability criteria proposed in theoretical analysis.The multiphase Riemann problem is a challenging multiphase problem in ship and ocean engineering, which is usually observed in underwater explosion. In this section, the Godunov-type SPH algorithm proposed by Sirothin and Yoh is combined with five kinds of single-phase approximation Riemann solvers (LLXF, ROE, HLLE, HLLC, DUCO) and three kinds interface approximation Riemann solvers (ROE, LRS, RRS). Four numerical examples, including air-air shock tube, air-helium shock tube, air-water shock tube and 2D underwater explosion problem, are presented. The results indicate that LLXF and HLLE get worse results than other Riemann solvers. It is also shown that the pressure discontinuity may happen to RRS.