Simulation and Analysis of Joint Transformation and Diffusion Dynamics in Irregular Domains : Application to Computational Modeling of Microbial Decomposition in Porous Media

Résumé

Many computational modeling challenges, particularly within the scope of natural phenomena, can be represented by coupled transformation and diffusion processes occurring in complex (3D) geometries. The spatialization of dynamics through numerical simulations provides a significantly improved understanding of process behaviors as they relate to the geometry in which they occur. This thesis presents a general framework for simulating coupled transformation and transport processes within any domain contained within a voxelized 3D representation. The proposed methodology describes the 3D domain of the dynamics through a hierarchy of attributed relational graphs. These graphs are constructed using advanced geometrical modeling methods. Transformation processes are assumed to occur locally at each graph node, while transport processes are modeled as mass exchange between adjacent graph nodes using Fick's law, which governs the relationship between diffusion flux and concentration gradients. To simulate these dynamics efficiently, we propose numerically stable schemes that reduce the computational complexity by focusing on graph updating instead of solving the corresponding Partial Differential Equations (PDEs) directly. Local adaptive diffusional conductance coefficients are incorporated into the graph to accurately represent the heterogeneity of the medium and the variability of transport properties between connected spatial units. In order to improve transport simulation, we use data-driven approach to calculate these coefficients accurately. The graph updating significantly lowers simulation costs, particularly in real-world applications where sensor data describing the spatial domain often result in extremely large meshes, making direct PDE solving computationally impossible. Moreover, this methodological framework based on valuated graph updating allow to take into account temporal changes of the domain by updating the graph structure. This general framework for computational modeling is applicable to a wide range of natural phenomena in irregular geometries. Its validation is demonstrated in the context of simulating diffusion and microbial decomposition in porous media derived from 3D computed tomography images. Specifically, we show that the framework reproduces a validated model of microbial decomposition of organic matter in soil, consistent with empirical data. The results highlight the framework's ability to handle complex transformation and diffusion processes inherent in real-world systems while maintaining computational efficiency. Additionally, we conduct a mathematical analysis of microbial decomposition dynamics, formulating the model as a nonlinear parabolic PDE and proving the existence of a global attractor, which ensures the long-term stability of the system.

Citer ce document

Accès au document

Ce document est hébergé sur son dépôt institutionnel d'origine.

Auteur(s)

Statistiques

Consultations : 3

Téléchargements : 0