Accelerated Finite Volume Schemes for Dynamic Convection-Dominant Power-Law Fluid Flows

This work evaluates the benefits of using the Anderson acceleration method in a finite volume context to solve convective-dominant power-law non-Newtonian fluid flows. We use a pressure-correction fractional step approach adapted to the finite volume method as a segregation strategy with the Picard linearization scheme. We evaluate the accuracy and performance of the Anderson method when we use TVD and non-TVD convective schemes. The work emphasizes algorithmic and programming aspects. We conduct several numerical tests to support the findings and evaluate the sensitivity of the methods concerning numerical parameters. First, we evaluate the convective schemes when solving two problems with analytical solutions to validate the implementation and accuracy. Subsequently, we use the Anderson acceleration method to solve the square lid-driven cavity flow problem for a steady case defined by Re =7500 and for unsteady solutions defined by Re =10,000 and 20,000. In this case, we analyze the robustness and performance of the schemes when solving nonlinear convection-dominant flows. Finally, we solve the lid-driven cavity flow problem for power-law fluids of shear-thinning and shear-thickening behavior defined by a power-law index n=0.5 and n=1.5. In this last case, we resolve a steady flow defined by Re = 5000, and then, we evaluate the methods to approximate unsteady solutions defined by Re = 15,000 with n=0.5 and Re = 25,000 with n=1.5. As the most important result, we reduce the number of nonlinear iterations using Anderson by 91.6% in the steady case and 79.9% in the time-dependent one in the Newtonian case. In the case of shear-thinning and shear-thickening fluids, the nonlinear iterations were reduced up to 49.7% and 64.3% when using acceleration in an unsteady, highly convective flow. © 2024 Elsevier B.V.