Giesekus fluid flow in a curved pipe based on Gauss–Radau spectral method

This study utilizes the Chebyshev–Fourier spectral collocation method to investigate the flow characteristics of Giesekus fluid in a curved pipe. Gauss–Radau collocation points are employed to avoid node placement at the singular point, and artificial diffusion terms are introduced into the constitutive equations to ensure the stability of the numerical solutions at higher Weissenberg numbers. The research explores the influence of physical parameters such as Reynolds number, curvature ratio, Weissenberg number, and mobility factor α on flow characteristics. As the curvature increases, the negative region of the second normal stress difference propagates toward the center, while the maximum positive region diminishes in proximity to the right wall. An increase in the mobility factor α intensifies shear-thinning phenomena, thereby significantly enhancing axial convective transport.