Simulating structure formation in soils across scales using discontinuous Galerkin methods

Viac o knihe

This thesis focuses on the mathematical modeling, analysis, and numerical realization of microaggregates in soils, which are fundamental building units with sizes in the range of a few hundred micrometers. Understanding their evolving three-dimensional structure is essential for modeling key soil parameters, such as diffusivities and flow paths, relevant in CO2 sequestration and oil recovery. The insights gained from this model are applied to larger scales for practical applications, as field-scale simulations that resolve pore-scale details are often economically unfeasible. The work compares diffusivity parameterizations with mathematically rigorous results and offers improvements to existing formulas in the literature. A critical aspect of this research is the application of an appropriate numerical method for in silico implementation of the model. The local discontinuous Galerkin (LDG) method is identified as suitable due to its local mass conservation and stability with discontinuous data, which may arise from discrete geometric movements or sharp phase boundaries. The thesis rigorously demonstrates these advantages and enhances the method by reducing the linear system of equations from discretization, achieving a significant reduction in computational costs without compromising the order of convergence.