Enhanced Nonlinear Solvers for Shear-Dependent Viscosity Models in Fluid Dynamics

Nonlinear constitutive relations arise frequently in fluid mechanics, especially in flows of complex or non-Newtonian fluids where viscosity depends on deformation rates. This paper develops and analyzes a robust solution strategy for a representative nonlinear equation obtained from the steady, fully-developed flow of a shear-thinning fluid in a channel. The governing equation reduces to a nonlinear ordinary differential equation whose nonlinearity couples momentum transport with a rate-dependent effective viscosity. We introduce a hybrid fixed-point and Newton correction scheme, prove its convergence properties under physically realistic conditions, and evaluate its performance against standard iterative methods. The proposed approach shows significant improvements in convergence speed and stability, particularly in regimes where classical Newton iteration fails due to strong degeneracy in the viscosity law.

کلیدواژه ها:

Fluid Dynamics ، Nonlinear Equation ، Differential Equation