Numerical simulations of immiscible generalised Newtonian fluids

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Nikiforakis, Nikolaos  ORCID logo
Almgren, A 

We present a numerical methodology for three-dimensional large-scale simulations of two-fluid flow for generalised Newtonian fluids exhibiting non-Newtonian behaviour such as a non-zero yield stress and power-law dependency on strain-rate. The incompressible continuity and Cauchy momentum equations, along with appropriate rheological models, are solved using a computational framework initially developed at Lawrence Berkeley National Laboratory. The solver uses second-order Godunov method- ology for the advective terms and semi-implicit diffusion in the context of an approximate projection method to evolve the system in time. We have extended the algorithm to en- able the simulation of Herschel-Bulkley fluids by means of a mathematical regularisation of the constitutive equation which describes the fluid rheology. Additionally, interfaces between fluids with different properties are treated using a passively advected indicator function. The performance of the software is validated for two-dimensional displacement flow and tested on a three-dimensional viscoplastic dambreak.

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Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
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EPSRC (1645917)
Funding and technical support from BP through the BP International Centre for Advanced Materials (BP-ICAM) which made this research possible.