Application of a projection method for simulating flow of a shear-thinning fluid

Masoud Jabbari*, James McDonough, Evan Mitsoulis, Jesper Henri Hattel

*Corresponding author for this work

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In this paper, a first-order projection method is used to solve the Navier–Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity. The flow structure in a cavity of aspect ratio δ = 1 and Reynolds numbers (100, 400, 1000) is compared with existing results to validate the code. We then apply the developed code to flow of a generalised Newtonian fluid with the well-known Ostwald–de Waele power-law model. Results show that, by decreasing n (further deviation from Newtonian behaviour) from 1 to 0.9, the peak values of the velocity decrease while the centre of the main vortex moves towards the upper right corner of the cavity. However, for n = 0.5, the behaviour is reversed and the main vortex shifts back towards the centre of the cavity. We moreover demonstrate that, for the deeper cavities, δ = 2, 4, as the shear-thinning parameter n decreased the top-main vortex expands towards the bottom surface, and correspondingly the secondary flow becomes less pronounced in the plane perpendicular to the cavity lid.
Original languageEnglish
Article number124
Issue number3
Number of pages16
Publication statusPublished - 2019

Bibliographical note

Copyright 2019: by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (


  • Lid-driven cavity
  • Projection method
  • Shear-thinning
  • Aspect ratio
  • Re numbers

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