Abstract
A combined scheme for the solution of the Cauchy equation of motion and the Phan-Thien/Tanner (P-T/T) constitutive equation is developed to solve the nonlinear problem of pressure and stress induced non-Newtonian flow, known as a (P,U,t) system. We start with the solution of the Navier-Stokes equations to obtain the initial flow conditions, we then solve the P-T/T equation using the initial and boundary conditions to simulate the stress and pressure fields for the visco-elastic regime. Finally, we solve the full nonlinear (P,U,t) system of Cauchy; P-T/T iteratively.
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