High-Order Splitting Scheme for Simulating Regularized Bingham Fluid Flow Using Spectral Element Methods

This study presents a high-order splitting scheme for simulating regularized Bingham fluid flow, aiming to enhance accuracy while reducing computational cost. The proposed method effectively handles the nonlinear stress–strain relationship using a spectral element method (SEM) for spatial discretization and an Adams–Bashforth scheme for time integration. A velocity correction-based splitting approach is employed for efficient pressure-velocity coupling. Compared with lower-order methods, our approach maintains high accuracy with significantly improved computational efficiency. The method is validated against a semi-analytical Poiseuille flow solution. We investigate the effects of Reynolds and Bingham numbers on velocity profiles, pressure drop, stress, and apparent viscosity. Results confirm the linear stress behavior in non-yielding regions, providing deeper insights into regularized Bingham fluid dynamics.