# Iterative schemes for surfactant transport in porous media

## TL;DR

This paper develops and analyzes iterative numerical schemes for modeling surfactant transport in variably saturated porous media, focusing on convergence, efficiency, and performance through various linearization techniques.

## Contribution

It introduces and compares monolithic and splitting schemes based on Newton, Picard, and L-scheme linearizations for coupled surfactant and water flow equations.

## Key findings

- Schemes converge under certain conditions
- Splitting schemes are computationally efficient
- Linear systems have manageable condition numbers

## Abstract

In this work we consider the transport of a surfactant in a variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three linearization techniques are discussed: the Newton method, the modified Picard and the L-scheme. Based on these, monolithic and splitting schemes are proposed and their convergence is analyzed. The performance of these schemes is illustrated on four numerical examples. For these examples, the number of iterations and the condition numbers of the linear systems emerging in each iteration are presented.