Modelling wall shear stress in small arteries using the Lattice Boltzmann method: influence of the endothelial wall profile.

In order to address the problem of blood flow over the endothelium in small arteries, the near-endothelial region is here studied in more detail. The method used is a finite-volume discretisation of a Lattice Boltzmann equation over unstructured grids, named unstructured Lattice Boltzmann equation (ULBE). It is a new scheme based on the idea of placing the unknown fields at the nodes of the mesh and evolving them based on the fluxes crossing the surfaces of the corresponding control volumes. The study shows a significant variation and a high sensitivity of wall shear stress to the height of the endothelium corrugation and the presence of erythrocytes. The latter were modelled as deformable, viscous particles within a fluid continuum.

A local lattice Boltzmann method for multiple immiscible fluids and dense suspensions of drops.

The lattice Boltzmann method (LBM) for computational fluid dynamics benefits from a simple, explicit, completely local computational algorithm making it highly efficient. We extend LBM to recover hydrodynamics of multi-component immiscible fluids, while retaining a completely local, explicit and simple algorithm. Hence, no computationally expensive lattice gradients, interaction potentials or curvatures, that use information from neighbouring lattice sites, need to be calculated, which makes the method highly scalable and suitable for high performance parallel computing. The method is analytical and is shown to recover correct continuum hydrodynamic equations of motion and interfacial boundary conditions. This LBM may be further extended to situations containing a high number (O(100)) of individually immiscible drops. We make comparisons of the emergent non-Newtonian behaviour with a power-law fluid model. We anticipate our method will have a range applications in engineering, industrial and biological sciences.