Mesoscale simulations: Lattice Boltzmann and particle algorithms

I introduce two mesoscale algorithms, lattice Boltzmann and stochastic rotation dynamics, and show how they can be used to investigate the hydrodynamics of complex fluids. For each method I describe the algorithm, show that it solves the Navier–Stokes equations, and then discuss physical problems where it is particularly applicable. For lattice Boltzmann the examples I choose are phase ordering in a binary fluid and drop dynamics on a chemically patterned surface. For stochastic rotation dynamics I consider the hydrodynamics of dilute polymer solutions, concentrating on shear thinning and translocation across a barrier.