The lattice density for a Navier-Stokes lattice (population which approximates NSE) can in general be initialized with unity.

Please note that dependent on what you are simulating, and which model you are using the physical densities of each lattice have separated meanings.

This means that the lattice densities are kinetic densities in the first place and are only mapped one-to-one on macroscopic conservables if constructed to do so.

For e.g. Free Energy Model, the lattice densities of the second (and maybe third for ternary systems) are macroscopic variables (order parameters) in the additional Cahn-Hilliard equations.

These variables are hence not directly the component densities, but instead recover them by a simple additive relation.

Dependent on exactly these relations the additional Cahn-Hilliard lattice densities should be initialized (see e.g. the microFluidics2d Example in OpenLB).

For more information please have a look at the user guide and the standard literature for Multiphase/Multicomponent LBM (e.g. Krüger et al. 2017 “The Lattice Boltzmann Method” Chapter 9).

BR

Stephan