An improved weakly compressible SPH method for simulating 2D multiphase flows with complex interface and large density ratios

This paper develops an improved weakly compressible smoothed particle hydrodynamics (SPH) method for simulating multiphase flows with complex interface and large density ratios. Surface tension is computed using a continuum surface force method along with a kernel gradient correction algorithm, thereby improving the numerical precision of normal vectors and curvatures. To maintain a uniform particle distribution and prevent instabilities resulting from particle stretching, a particle shifting technique is implemented. Additionally, an anisotropic interfacial repulsion force is introduced at the multiphase interface to create smooth phase boundaries and mitigate issues related to particle penetration. The efficacy of the method is demonstrated through simulations of various scenarios including the deformation of a square droplet, the Rayleigh-Taylor instability, the lock-exchange phenomena, a single rising bubble, and two rising bubbles. By comparing the results with analytical solutions and existing literature data, the accuracy and consistency of the numerical results are confirmed. These comparisons demonstrate that the improved multiphase SPH method developed in this study can effectively track deformable phase interfaces and simulate multiphase flows with complex interfaces and large density ratios in a stable way.