Lattice Boltzmann Method for Mathematical Morphology: Application to Porous Media

The LBM (Lattice Boltzmann Method) is often used in CFD (Computational Fluid Dynamics) for efficient fluid flow simulations. Computation of the permeability of a porous media from direct simulations is a common application which benefits from the ability of the LBM (Lattice Boltzmann Method) to embed porosity parameters. The MM (Mathematical Morphology) is widely used in image processing as the theoretical aspects guaranty robust algorithms for geometrical characterization of shapes appearing in images. The MM is commonly used to compute porosity from porous media images. The union of these two methods has been recently done through the LB3M (Lattice Boltzmann Method for Mathematical Morphology). The present work extends the LB3M to the extraction of porosity and pores segmentation from images. In order to benefit from the full capacity of the LB3M, it is necessary to reformulate and adjust the algorithms in a new paradigm. Thus, the underlying concept and algorithms required for computing the different previous information are detailed. Moreover, a comparison is provided between the permeability resulting from the CFD and MM both implemented by using the LBM. To sum up, this work emphasizes the full capacity of the LB3M to obtain complex transformations and operations issued from the MM theory through completely new and innovative algorithms. The herein challenge is to highlight the abilities of the LB3M to match with physical phenomenons. Indeed, the LB3M keeps the advantages from the MM such as a complete theory, fast convergence, scalability, robustness, etc. while adding the power of the LBM: statistical physics origins, partial differential equation solver, intrinsic properties of parallelization, efficiency, etc.