Comparison of Numerically Stable Methods for Implementation of a Double Porosity Model with First-Order Reaction Terms

Abstract

The influence of barometric cycling on gas transport through complex media can be described using a double porosity model. Here vertical channels simulate the effect of cracks that pass through homogeneous regions of media. The cracks are coupled to the atmosphere and act as boundaries for the sections of homogeneous media. Convection–diffusion models are then used to simulate gas transport through the coupled system. This approach has been used to model soil aeration, subsurface movement of volatile compounds, and the migration of gases to the surface after below ground nuclear detonations. In the present work, we describe four stable numerical methods that can be used to implement the double porosity model when first-order reactions produce and consume the gaseous species of interest. We find that all four methods satisfy analytical crosschecks and agree to at least seven digits of precision. An iterative solver based on Newton’s method is found to be optimal as it is easily scalable to 3-D models and to multithreaded execution.