skip to content

Laboratory for Scientific Computing


The oil and gas industry uses many complex fluids in a wide range of applications. These fluids are usually non-Newtonian in character and possess a variety of characteristics which are not well understood. Many of these characteristics originate from local microscopic interactions in the fluid, particularly in complex fluids containing particle or polymer molecule additives. In such fluids the interactions between the suspended material, the suspension fluid, and the domain boundaries give rise to non-Newtonian characteristics of the bulk fluid.


This project is sponsored by Schlumberger Cambridge Research 

The challenge

An efficient meshing strategy is combined with an exact viscoplastic solver to reduce the required computational effort as much as possible.

In contrast to Newtonian fluid, very little numerical work has been done on particle laden viscoplastic fluid flows. Many successful strategies for large scale suspension simulation in Newtonian fluids rely on superposition principles to make large scale computations tractable, which are not applicable to the non-linear viscoplastic system. Coarse-grained approaches for Newtonian fluids use lubrication force models as sub-grid-scale models for the under-resolved particle interactions. However, we found that such lubrication models cannot be straightforwardly applied to general flow conditions. As a result, in order to simulate particle flows at scale and without sub-grid-scale modelling, we need to combine an efficient meshing strategy with an exact viscoplastic solver to reduce the required computational effort as much as possible.

The research

We made use of the Overture ( package developed by Henshaw et al., a library for solving partial differential equations on overset, curvilinear meshes. Each particle in our system is represented by its own curvilinear mesh, overset on a Cartesian background mesh, thereby enabling both efficient mesh generation and grid point clustering near the particle surface to capture the viscous boundary layer. This is combined with a widely adopted Augmented Lagrangian solution method for genuinely non-smooth treatment of the viscoplastic system.


We looked at both small-scale two particle systems and larger suspensions with O(100) particles, investigating a variety of behaviours, including: the viscoplastic lubrication force between two cylinders; particle clustering and critical yield numbers in sedimentation experiments; effective viscosity of sheared suspensions. To the left we show two views of a sedimentation cluster: the left panel shows particle velocity vectors overlaid on a colourmap showing the fluid speed; the colourmap in the right panel provides information on the fluid structure, showing where the fluid is unyielded (white), rotational (black), strained (yellow) and sheared (orange/mauve). These sedimentation simulations guided experiments at the industrial research lab, reproducing our findings.