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Keywords
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Spectral element methods, viscoplastic fluids, Bingham fluid, regularization technique, high-order splitting scheme
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Abstract
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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.
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