Objective:

The modeling of flow sand pollutants faces defiant challenges, ranging from the definition of complex geometries to the convergence of the algorithm and determination of the model parameters. The method presented here faces this problem through a joint application of the Lattice-Boltzmann methods and finite differences. The numerical solution of the both Navier-Stokes, and Advection Diffusion equations allow simulating the spread levels of spatial and temporal contamination in a water source.

Methodology:

The method solved the Navier-Stokes equations using the Lattice Boltzmann method, which provides the fluid velocities vector field. The solution of diffusion - advection equation by finite difference requires this known velocity field. The C++ encoded solution, first digitizes the map, labeling each pixel on the map as fluid or solid. The code uses the digital image to setup geometry the flow zone, then simulate the fluid dynamics and concentration of the contaminant. The comparison between the analytical solutions of ideal advective -diffusive models with the obtained through this method, allow the measurement of the method reliability. Applied to a section of the Sogamoso river Colombia, the algorithm yielded the agent’s velocity, pressure, and concentration.

Results:

It was found that the advective term predominates in each of the sections of the Sogamoso River. However, there is a section in the upper section, where the difussive component predominates. This happens because there the speed very low.

Conclusions:

The obtained results point out the reliability, stability, and robustness of the method to simulate

advection-diffusion phenomena in bodies with irregular geometries.