A Python implementation in graphic processing unit of a lattice Boltzmann model for unstable three-dimensional flows in immersed permeable media

The implementation of a lattice Boltzmann model for three-dimensional permeable media with localized drag forces is presented. The model was previously introduced for two-dimensional geometries and follows the basics of the immersed boundary method. Permeable flows are much less stable than their counterparts in porous media and generally produce large coherent flow structures, such as vortex lines, rolls, and wakes. In addition, in permeable media, the small-scale geometry often needs to be represented to a high degree of detail in order to capture certain transport phenomena, such as micro-convection or pollination. Hence, both calculation speed and memory requirements are under strain. The present model was implemented in a graphic processing unit showing excellent performance in the calculation of stable and unstable flows in a rectangular channel partially obstructed by an array of parallel wires. In particular, the model is able to deal with small and medium spatial scales without losing the heterogeneous nature of permeable flows in the homogenization process. The algorithm to manage memory issues is described in detail, and the results of the test case for stable and unstable conditions show the capability of the method to simulate these types of flows.