We review recent advances on the mesoscopic modeling of water-like fluids, based on the lattice Boltzmann (LB) methodology. The main idea is to enrich the basic LB (hydro)-dynamics with angular degrees of freedom responding to suitable directional potentials between water-like molecules. The model is shown to reproduce some microscopic features of liquid water, such as an average number of hydrogen bonds per molecules (HBs) between 3 and 4, as well as a qualitatively correct statistics of the hydrogen bond angle as a function of the temperature.

One of the promising frontiers of bioengineering is the controlled release of a therapeutic drug from a vehicle across the skin (transdermal drug delivery). In order to study the complete process, a two-phase mathematical model describing the dynamics of a substance between two coupled media of different properties and dimensions is presented. A system of partial differential equations describes the diffusion and the binding/unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed.

Duchenne muscular dystrophy (DMD) is a genetic disease that results in the death of affected boys by early adulthood. The genetic defect responsible for DMD has been known for over 25 years, yet at present there is neither cure nor effective treatment for DMD. During early disease onset, the mdx mouse has been validated as an animal model for DMD and use of this model has led to valuable but incomplete insights into the disease process.

Recent developments of the lattice Boltzmann method for large-scale haemodynamic applications are presented, with special focus on multiscale aspects, including the self-consistent dynamics of suspended biological bodies and their coupling to surface structures, such as the glycocalyx, in the proximity of endothelium using unstructured grids.

Fluid flow through porous media is of great importance for many natural systems, such as transport of groundwater flow, pollution transport and mineral processing. In this paper, we propose and validate a novel finite volume formulation of the lattice Boltzmann method for porous flows, based on the Brinkman-Forchheimer equation. The porous media effect is incorporated as a force term in the lattice Boltzmann equation, which is numerically solved through a cell-centered finite volume scheme. Correction factors are introduced to improve the numerical stability.

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows.