Lattice-Boltzmann simulation of liquids forced through a percolative path.

The simulation is a single-relaxation time Lattice Boltzmann simulation in two dimensions. The lattice size is 512x256, where the middle obstacle that contains the porous cavernous paths is 256x256. The lattice is periodic in all directions, but the fluid (due to the nature of the porous plug and the force) is pretty much flowing from left to right. Inside the plug the flow is strictly from left to right since paths do not cross the horizontal upper and lower boundaries. The porosity of the medium is 0.49888846545 in the plug region (as measured in the 256x256 middle section).

The general parameters are that the system is driven by a very small force that points towards the right. Also, the injection of force is a single vertical line located in the leftmost column of the simulation (right in the middle of the bulk).

The simulation starts with a random population of (average) density 1 per site. After about 10^6 steps, the flux approaches equilibrium, which is the one shown below. The relaxation time is 0.65 giving a viscosity of 0.05.

(Clickable pictures)

Porosity (blue) Magnitude of Total Momentum.
(see colormap on the right for relative intensity)

In the next table, there are representations for the magnitude of the total momentum side-by-side with the flux represented by arrows. The flux has been averaged over a grid of 4x4 sites. In the flux pictures, arrows smaller (and bigger) than appropriate thresholds are not shown.

Magnitude of the Total Momentum Vectorial flux (ave over 4x4 grid)
Magnitude of P (close up) Flux (close up)

In the next table, there are pictures that correspond to momentum decomposition.

X component of Momentum Y component of Momentum

The simulation can be run and visualized interactively using the front-end of the program, shown below. Background jobs are independent of the graphics and front-end part of the program.