A NUMERICAL CASE-STUDY OF A NON-NEWTONIAN FLOW PROBLEM

This paper addresses some of the theoretical aspects involved in the numerical study of non-Newtonian flow problems. We consider the second-order Rivlin-Erickson constitutive model due to the simple differential form that emerges for the system of equations that govern the flow when expressed in stream function-vorticity variables. This model describes slightly elastic fluids that exhibit a constant viscosity behavior. A steady two-dimensional flow is studied through a planar contraction geometry. An auxiliary variable is introduced into the problem formulation producing a nonlinear system of differential equations comprising two elliptic equations and one hyperbolic equation. This system is discretized by finite difference methods and the resulting system of nonlinear algebraic equations is solved iteratively by successive substitutions. The simple structure of this iteration permits a convergence analysis.