Higher-Order Recurrent Finsler Geometry and Anisotropic Flow Modelling with CFD Applications

Abstract

In this work, a unified high-level framework that links anisotropic flow via higher-order recurrence structures with Finsler geometry is developed. It focuses on the connections between Weyl projective and concircular curvature tensors in extended second-order recurrent and birecurrent Finsler spaces. By obtaining new tensorial relations and strict necessary and sufficient conditions, classical recurrence theory is expanded. To confirm applicability, CFD simulations of viscous flow in curved pipes with varying curvatures and intake conditions are performed. The results demonstrate significant directional dependency in velocity and wall shear stress. The results are consistent with the proposed geometric model, indicating a close relationship between advanced differential geometry and anisotropic fluid behavior with implications for modified gravity and cosmology.