Three-dimensional single framework multi-component lattice Boltzmann equation method for vesicle hydrodynamics

We develop a three dimensional immersed boundary chromodynamic multi-component lattice Boltzmann method capable of simulating vesicles, such as erythrocytes. The presented method is encapsulated in a single framework, where the application of the immersed boundary force in the automatically adaptive interfacial region results in correct vesicle behaviour. We also set-down a methodology for computing the principal curvatures of a surface in a three-dimensional, physical space which is defined solely in terms of its surface normal vectors. The benefits of such a model are its transparent methodology, stability at high levels of deformation, automatic-adaptive interface and potential for the simulation of many erythrocytes. We demonstrate the utility of the model by examining the steady state properties, as well as dynamical behaviour within shear flow. The stability of the method is highlighted through its handling of high deformations, as well as interaction with another vesicle.