Study on SPH Viscosity Term Formulations

Featured Application: The proposed study contributes to the mesh-free numerical modeling field through the examinations of several viscosity term formulations. By simulating benchmark viscosity-dominated flows in engineering practice, the optimal viscosity scheme has been found to work with the Smoothed Particle Hydrodynamics (SPH) method.

Abstract: For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified.