This study is concerned with the numerical modelling of thixotropic and non-thixotropic materials in contraction-expansion flows at high Weissenberg number (We). Thixotropy is represented via a new micellar time-dependent constitutive model for worm-like micellar systems and contrasted against network-based time-independent PTT forms. The work focuses on steady-state solutions in axisymmetric rounded-corner 4:1:4 contraction-expansion flows for the benchmark solvent-fraction of beta = 1/9 and moderate hardening characteristics (epsilon = 0.25). In practice, this work has relevance to industrial and healthcare applications, such as enhanced oil-reservoir recovery and microfluidics. Simulations have been performed via a hybrid finite element/finite volume algorithm, based around an incremental pressure-correction time-stepping structure. To obtain high-We solutions, both micellar and PTT constitutive equation f-functionals have been amended by (i) adopting their absolute values appealing to physical arguments (ABS-correction); (ii) through a change of stress variable, Pi = tau(p) + (eta(p0)/lambda(1))I, that aims to prevent the loss of evolution in the underlying initial value problem; and finally, (iii) through an improved realisation of velocity gradient boundary conditions imposed at the centreline (VGR-correction). On the centreline, the eigenvalues of Pi are identified with its Pi-stress-components, and discontinuities in Pi-components are located and associated with the f-functional-poles in simple uniaxial extension. Quality of solution is described through tau(rz) N-1 and N-2 (signature of vortex dynamics) stress fields, and Pi-eigenvalues. With {micellar, EPTT} fluids, the critical Weissenberg number is shifted from critical states of We(crit) = {4.9,220} without correction, to We(crit) = {O(10(2)), O(10(3))} with ABS-VGR-correction. Furthermore, such constitutive equation correction has been found to have general applicability. (C) 2014 Elsevier B.V. All rights reserved.