Lattice-gas and lattice-Boltzmann models of miscible fluids

We introduce new lattice-gas and lattice-Boltzmann models for simulating miscible fluids in two dimensions. The inclusion of a nonlocal interaction produces a lattice gas with lower diffusivity than achieved before. To overcome some observed unphysical properties of this lattice gas, we introduce a lattice-Boltzmann analogue of the model. We first formulate a miscible two-component lattice-Boltzmann model with local interactions only, and show that its diffusivity is determined by an eigenvalue of the linearized collision operator. Diffusivity is then reduced by including nonlocal interactions. The utility of the model is demonstrated by a simulation of two-dimensional viscous fingering.