Simulations of viscous flows of complex fluids with a Bhatnagar, Gross, and Krook lattice gas

We address the question of using a lattice gas method to study flows of complex fluids, such as non-Newtonian or miscible fluids. A Bhatnagar, Gross, and Krook lattice technique provides a tool to simulate the flow of one fluid and the diffusion of a tracer in that fluid. We extend the technique to flows in which the viscosity is space and time dependent. This approach is suitable for non-Newtonian fluids (shear dependent viscosity) and miscible fluids (concentration dependent viscosity). The modified scheme is tested on physical flow situations, analytically tractable for the sake of comparison.