Smoothed Particle Hydrodynamics Simulation of Bingham Fluid Flow in Obstructed Channels: A Comparative Study of Viscosity Regularization Models

This study investigates pressure-driven Bingham fluid flow in two-dimensional channels with various obstacle configurations using the smoothed-particle hydrodynamics (SPH) method. Two benchmark regularization models are employed: the Papanastasiou model and the Bercovier and Engelman (B&E) model. As an extension of the existing model, we here propose its modified versions by introducing an additional parameter to improve flexibility near the yield point and enhance numerical robustness. Simulations were conducted in straight channels for three obstacle configurations: a single rectangular obstacle in the middle of the channel and in-phase and out-of-phase configurations. In the unobstructed case, validation against analytical solutions showed that the SPH method achieved an average error of about in steady-state flow across all regularization models. Comparisons of accuracy and computational time revealed that the modified B&E model with a flexibility parameter of 5 offers the best balance of precision and efficiency. This finding led us to choose the modified B&E model for our obstructed-channel simulations. We found that the single middle rectangular obstacle induced particle accumulation upstream and accelerated flow near the walls, and the in-phase configuration reduced fluid velocities more than the out-of-phase case, achieving a faster transition to steady state. These results demonstrate the effectiveness of modified viscosity models in improving SPH simulations of viscoplastic flows and serve as a guide for selecting efficient models in complex geometries.