Accurate implicit moving particle simulation method with angular momentum conservation for high-viscous free-surface flow

Particle methods, benefiting from the Lagrangian meshfree framework, have gained widespread application in free-surface flow simulations. Nonetheless, accurately modeling high-viscosity fluids remains a persistent challenge. In this study, we propose a new implicit moving particle simulation (IMPS) method specifically designed to address the complexities associated with high-viscous free-surface flows, tackling two main issues. Firstly, unlike the traditional Laplacian model, where orthogonal velocity components are treated as independent variables, this method enforces the velocity divergence-free constraint when discretizing the viscous term, effectively coupling the velocity components. This coupling is crucial for conserving angular momentum, especially in high-viscosity scenarios. Secondly, to overcome the time step restrictions imposed by high viscosity, a novel implicit calculation algorithm has been developed. This algorithm enables the simultaneous and implicit solution of pressure and velocity, ensuring the precise application of both free-surface and wall boundary conditions. The effectiveness of the IMPS method is rigorously verified through simulations, including a rotational flow in a circular pipe and a square fluid dropping from a platform. The results indicate that the developed method successfully captures the dynamics of high-viscous free-surface flows, demonstrating its potential for broader applications.