# Iterative schemes for surfactant transport in porous media

```@article{Illiano2019IterativeSF,
title={Iterative schemes for surfactant transport in porous media},
journal={Computational Geosciences},
year={2019},
volume={25},
pages={805 - 822}
}```
• Published 1 June 2019
• Mathematics
• Computational Geosciences
In this work, we consider the transport of a surfactant in 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 five numerical examples. For…
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## References

SHOWING 1-10 OF 63 REFERENCES

• Mathematics
SIAM J. Numer. Anal.
• 2013
The numerical analysis of an upscaled model describing the reactive flow in a porous medium, using the lowest order Raviart--Thomas elements, yields an existence proof for the solution of the model in mixed variational formulation and proves the convergence to the continuous formulation.
In this paper, the numerical approximation of a nonlinear diffusion equation arising in contaminant transport is studied. The equation is characterized by advection, diffusion, and adsorption.
• Environmental Science, Engineering
• 1998
A numerical model for the simulation of flow and transport of organic compounds undergoing bacterial oxygen- and nitrate-based respiration is presented. General assumptions regarding microbial
• Engineering
• 2017
A universally robust and accurate solution methodology has not yet been identified that is applicable across the range of soils, initial and boundary conditions found in practice, and alternative solution approaches or methods are needed.
A robust, efficient, and reliable linear relaxation approximation scheme for nonlinear degenerate convection-diffusion model problem having an application in groundwater aquifer and petroleum reservoir simulation is designed.
• Mathematics
SIAM J. Numer. Anal.
• 2000
We present an analysis of expanded mixed finite element methods applied to Richards' equation, a nonlinear parabolic partial differential equation modeling the flow of water into a variably saturated