The University of Southampton
University of Southampton Institutional Repository

# Multiscale mathematical modelling of water and solute movement in plant systems

Duncan, Simon Jack (2018) Multiscale mathematical modelling of water and solute movement in plant systems. University of Southampton, Doctoral Thesis, 196pp.

Record type: Thesis (Doctoral)

## Abstract

This thesis deals with multiscale mathematical modelling of water and solute movement in soil systems, with particular focus on the soil structures that are formed by agricultural practices. The ﬁrst mathematical model is developed to describe water movement in a generalised ridge and furrow soil system, which is coupled to dynamic surface water inﬁltration due to ponding. The model is based on a non-linear Darcy-Richards’ equation in pressure formulation to describe variably saturated soil. This model is then extended and coupled to an advective-diffusion equation for solute movement. Using the mathematical model, we compare water and solute movement in two soil structures: a ridge and furrow soil and a ﬂat ﬁeld soil. We highlight scenarios that increase the risk of solute leaching in both ﬂat ﬁeld and ridged soils. We also discuss the key factors affecting solute leaching in these systems. We then focus on the water dynamics in the regions of soil that contain crops. Using the Darcy-Richards’ equation for water movement, we apply multiple scale asymptotic homogenisation to derive an approximate set of equations that captures water movement around crops. We ﬁnd the approximate equations to be more computationally efﬁcient by a factor of O(102) when compared to the full equations. Extending this idea, we develop a mathematical model that captures crop growth and its effect on solute movement. The growth and development of the crops is dependent on the cumulative uptake of nutrients available to the plant. The soil is modelled as a poroelastic material that is able to deform due to crop growth. Special attention is paid to the reduction in void space, change in local volumetric water content and the impact on solute movement as the crops increase in size. Multiple scale asymptotic homogenisation is used to derive a set of approximate equations that describe macroscale nutrient movement and crop growth in the soil. This approach increases computational efﬁcient by a factor of O(103) while maintaining a percentage error of <∼ 2%.

Text
Simon Duncan Thesis - Version of Record

Published date: September 2018

## Identifiers

Local EPrints ID: 428620
URI: http://eprints.soton.ac.uk/id/eprint/428620
PURE UUID: 3f67cd46-f262-4c31-a791-a1ff6f6717f3
ORCID for Tiina Roose: orcid.org/0000-0001-8710-1063

## Catalogue record

Date deposited: 05 Mar 2019 17:30

## Contributors

Author: Simon Jack Duncan