Improved Implicit SPH Method for simulating free surface flows of power law fluids

Implicit smoothed particle hydrodynamics method has been proposed to overcome the problem that only very small time steps can be used for high viscosity fluids (such as power law fluids) in order to obtain a stable simulation. However, the pressure field is difficult to simulate correctly with this method because the numerical high-frequency noise on the pressure field cannot be removed. In this study, several improvements, which are the diffusive term in the continuity equation, the artificial viscosity and a simplified physical viscosity term in the momentum equation, are introduced, and a new boundary treatment is also proposed. The linear equations derived from the momentum equation are large-scale, sparse and positive definite but unsymmetrical, therefore, Conjugate Gradient Squared (CGS) is used to solve them. For the purpose of verifying the validity of the proposed method, Poiseuille flows with Newtonian and power law fluids are solved and compared with exact solution and traditional SPH. Drops of different fluid properties impacting a rigid wall are also simulated and compared with VOF solution. All the numerical results obtained by the proposed method agree well with available data. The proposed method shows the higher efficiency than traditional SPH and the less numerical noise on the pressure field and better stability than implicit SPH.