Related papers: Homogenization of a multiscale model for water tra…
Water flow in plant tissues takes place in two different physical domains separated by semipermeable membranes: cell insides and cell walls. The assembly of all cell insides and cell walls are termed symplast and apoplast, respectively.…
The water uptake by roots of plants is examined for an ideal situation, with an approximation that resembles plants growing in pots, meaning that the total soil volume is fixed. We propose a coupled water uptake-root growth model. A…
In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
In this paper, we first propose a coupled numerical model of unsaturated flow in soils and plant root water uptake. The Richards equation and different formulations are used in the developed numerical model to describe infiltration in root…
Understanding how submerged vegetation modifies the water surface is crucial for modeling momentum exchange between shallow waters and the atmosphere. In particular, quantifying its impact on the equivalent aerodynamic roughness of the…
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…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
An optimization-based strategy is proposed for coupling three-dimensional and one-dimensional problems (3D-1D coupling) in the context of soil-root interaction simulations. This strategy, originally designed to tackle generic 3D-1D coupled…
The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can help in assessing the plant's health, understanding its growth…
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…
In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of…
Ion transport in biological tissues is crucial in the study of many biological and pathological problems. Some multi-cellular structures, like smooth muscles on the vessel walls, could be treated as periodic bi-domain structures, which…
Root systems can influence the dynamics of evapotranspiration of water out of a porous medium. The coupling of evapotranspiration remains a key aspect affecting overall root behavior. Predicting the evapotranspiration curve in the presence…
Modeling unsaturated flow through soils with water uptake by plan root has many applications in agriculture and water resources management. In this study, our aim is to develop efficient numerical techniques for solving the Richards…
In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsaturated water flow through soils. The design of approximate…
In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells,…
In this paper we introduce an optimal control approach to Richards' equation in an irrigation framework, aimed at minimizing water consumption while maximizing root water uptake. We first describe the physics of the nonlinear model under…
This paper is concerned with the Richards equation in a heterogeneous domain, each subdomain of which is homogeneous and represents a rocktype. Our first contribution is to rigorously prove convergence toward a weak solution of…