Evaluating the Impact of Boundary Conditions on the MR-LBM

Resumo

The fluid flow investigation in heterogeneous porous media has several applications, such as in the oil
and gas industry. One of the problems is determining the permeability of the porous media. However, numerical
studies often employed simple geometric forms (spheres, cubes, cylinders) to represent the porous media. Complex
meshes are usually required when scans are employed to describe the porous media. The Lattice Boltzmann
Method (LBM) can address this problem without complicated meshes. Recently, the moment representation of the
LBM has gained interest due to its reduced memory requirements and increased speed. The reduced memory usage
is achieved by storing moments from 0th to 2nd order instead of the mesoscopic populations. This change also
reduces the bandwidth usage between the memory and the processor, which is a bottleneck for the LBM, thereby
increasing performance. However, boundary lattices will require additional arithmetic operations when conditions
other than a periodic need to be applied, leading to speed degradation. In simulations of a heterogeneous porous
media, many lattices are subjected to boundary conditions, and the probability of having a neighbor lattice affected
by it increases with a reduction in porosity. Additionally, cases with the same solid volume fraction can exhibit
different performances. This discrepancy arises because the effect of the boundary condition in the processing is
associated with the wet surface area. To investigate these parameters (solid volume fraction and wet surface area),
we build heterogeneous porous media using a Gaussian blur over a randomly generated domain. We varied the
porosity by tuning the threshold value while the standard deviation changed the surface area. The results
demonstrate that as the porosity decreases, the computational performance also decreases. However, once the
porosity reaches a certain threshold, the execution time decreases due to reduced total wet surface area, and the
number of fluid nodes reduces. Additionally, there is a direct correlation between the computational speed and the
standard deviation of the Gaussian blur for the wet surface area. With more lattices neighboring other solid lattices,
there is a reduction of boundary conditions being applied as well as the number of collision-streaming steps being
performed, resulting in improved performance.