Diagenetic modelling in Julia

This repository contains example codes to solve numerical PDEs in Julia. The goal is to reproduce the results from Ivan l’Heureux 2018. We’ll work from basics of solving PDEs to running the full model.

• Diffusion equation
• Advection equation
• Fiadeiro-Veronis scheme
• l’Heureux model

Architecture

In this implementation, readability is a primary concern. The target model has five long equations and more than 30 free parameters. It would be a shame if we have to mix the intricacies of numerical methods with the actual implementation of the model. When solving partial differential equations, this means that we may want to write the actual PDEs in a natural form, and then automatically generate the space descretisation for each equation. There is a set of Julia package called ModelingToolkit.jl and more specifically MethodOfLines.jl that implements a scheme like this, so we could end up using that. For now, using those would fall outside of the scope of the project due to time constraints (Learning how to use these and adapting the model could take a significant effort).

The ModelingToolkit has a nice tutorial on “Large Stiff Equations” that could be of use here.