Generic tool for numerical simulation of transformation-diffusion processes in complex volume geometric shapes: Application to microbial decomposition of organic matter

This paper presents a generic framework for the numerical simulation of transformation-diffusion processes in complex volume geometric shapes. This work follows a previous one devoted to the simulation of microbial degradation of organic matter in porous system at microscopic scale using a graph based method. The pore space is represented by an optimal ball network. We generalized and improved the MOSAIC method significantly and thus yielded a much more generic and efficient numerical simulation scheme. We proposed to improve the numerical explicit scheme presented in a previous paper by updating the valuated graph in parallel instead of sequentially. From this parallel numerical explicit scheme, we derived an implicit numerical scheme that very significantly reduced the computational cost of the simulation of the diffusion process. We validated our method by comparing the results to the ones provided by classical Lattice Boltzmann Method (LBM) within the context of microbial decomposition simulation. For the same datasets, we obtained similar results in a significantly shorter computing time (i.e., 10–15 min) than the prior work (several hours). Besides the classical LBM method takes around 3 weeks computing time. This paper presents through details the algorithmic and mathematical schemes used in a previous paper.