Improvements in highly viscous fluid simulation using a fully implicit SPH method

This study describes the application of two main improvements in highly viscous fluid simulations using the smoothed particle hydrodynamics (SPH) method: an implicit time integration scheme to overcome the problem of impractically small time step restriction and the introduction of air ghost particles to fix problems regarding the free surface treatment. This study adopts the incompressible SPH as a basis for the implementation of these improvements, which guarantees a stable and accurate pressure distribution. We verified the proposed implicit time integration scheme with simulations of pipe flow and the free surface treatment with a simple hydrostatic problem. As a result, the free surface of the hydrostatic problem became very smooth and stable. In addition, we conducted a variety of dam-break simulations to validate this proposed SPH method, as well as to analyze the density and divergence error. Finally, we demonstrate the potential of this method with the highly viscous vertical jet flow over a horizontal plate test, which features a complex viscous coiling behavior.