arXiv subjects

Stelian Ion

Publications and source records attributed to Stelian Ion.

8 recordsLinked to original sources

arXiv2025

ASTERIX: Module for modelling the water flow on vegetated hillslopes

The paper presents an open source software for numerical integration of an extended Saint-Venant model used as a mathematical tool to simulate the water flow from laboratory up to large-scale spatial domains applying physically-based principles of fluid mechanics. Many in-situ observations have shown that vegetation plays a key role in controlling the hydrological flux at catchment scale. In case of heavy rains, the infiltration and interception processes cease quickly, the remaining rainfall gives rise to the Hortonian overland flow and the flash flood is thus initiated. In this context, we also address the following problem: how do the gradient of soil surface and the vegetation influence the water dynamics in the Hortonian flow? The mathematical model and ASTERIX were kept as simple as possible in order to be accessible to a wide range of stakeholders interested in understanding the complex processes behind the water flow on hillslopes covered by plants.

cs.MS↗

arXiv2024

Water flow model on vegetated hillslopes with erosion

The water circulation in the Soil-Plant-Atmosphere continuum and particularly the soil erosion induced by water are problems of main concern in the new era of climate change. The present paper aims to provide a mathematical tool to investigate the water-soil and water-plant interactions involved in the complex process of water flow on plant-covered soil surfaces. Basically, the mathematical model consists of an extended Saint-Venant system of equations for water flow coupled with Hairsine-Rose equations for soil erosion. The classical Saint-Venant model is thus modified in order to take into account the presence of plants on the soil surface. A numerical approximation of the solution of our model is built using a Finite Volume Method for the discretization in space and a fractional time-step scheme to discretize the time variable and resulting time derivatives. Several properties of the scheme with physical relevance are also discussed and investigated. In order to validate both the model and the numerical method, and to see if essence of the reality is adequately reflected, a series of qualitative and quantitative tests are performed. Given that the mathematical model is flexible enough to reflect the variability of the environmental variables such as soil structure, soil surface roughness, or plant cover structure, each numerical experiment is constructed as an image of a target hydrological context. The dam break problem, flash floods, water-induced soil erosion in a catchment basin are all subjects of numerical analysis. It is shown that the presence of the plant cover drastically modifies the water dynamics and the distribution of the soil eroded particles and one can quantitatively evaluate such effects. The methods described in the paper can also help one to manage the environmental resources in order to avoid the water induced disasters.

physics.flu-dyn↗

arXiv2023

Analysis of the Effects of Curvature on the Solutions of Shallow Water Equations

The most used form of the Shallow Water Equations doesn't take into account the variation of the curvature of the base flow surface. In this paper, we compare the theoretical and numerical solutions of the standard model and with the solutions of an extended model and for a large class of base flow surfaces. We find that the solution of the standard model is still a good approximation for the extended model for many real life applications.

physics.flu-dyn↗

arXiv2020

Fluid Flow on Vegetated Hillslope

In this paper, we present a deduction of swallow water equations in the presence of vegetation based on spatial averaging techniques starting from the general principles of conservation of mass and momentum. For this purpose, we worked in the hydrostatic approximation of the pressure field and we considered certain hypotheses of kinematic and topographical nature and assumptions on the structure of the vegetation. Some elements of differential geometry necessary to facilitate the reading of the paper can be found in the Appendix.

math-ph↗

arXiv2019

A Shallow Water Model for Water Flow on Vegetated Hillslope

The hillslope hydrological processes are very important in watershed hydrology research. In this paper we focus on the water flow over the soil surface with vegetation in a hydrographic basin. We introduce a PDE model based on general principles of fluid mechanics where the unknowns are water depth and water velocity. The influence of the plant cover to the water dynamics is given by porosity (a quantity related to the density of the vegetation), which is a function defined over the hydrological basin. Using finite volume method for approximating the spatial derivatives, we build an ODE system which constitutes the base of the discrete model we will work with. We discuss and investigate several physical relevant properties of this model. Finally, we perform different quantitative validation tests by comparing numerical results with exact solutions or with laboratory measured data. We also consider some qualitative validation tests by numerically simulating the flow on a theoretical vegetated soil and on a real hydrographic basin.

physics.flu-dyn↗

arXiv2019

Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be ``small enough''). One difficulty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another difficulty is given by the fact that the construction of the solution assumes solving an equation which has no global solution. Finally, we present some cases to illustrate the existence and non-existence of the solution.

math.AP↗

arXiv2016

A Shallow Water Model for Hydrodynamic Processes on Vegetated Hillslope. Water Flow Modulus

math.AP↗

arXiv2014

A data porting tool for coupling models with different discretization needs

The presented work is part of a larger research program dealing with developing tools for coupling biogeochemical models in contaminated landscapes. The specific objective of this article is to provide the researchers a tool to build hexagonal raster using information from a rectangular raster data (e.g. GIS format), data porting. This tool involves a computational algorithm and an open source software (written in C). The method of extending the reticulated functions defined on 2D networks is an essential key of this algorithm and can also be used for other purposes than data porting. The algorithm allows one to build the hexagonal raster with a cell size independent from the geometry of the rectangular raster. The extended function is a bi-cubic spline which can exactly reconstruct polynomials up to degree three in each variable. We validate the method by analyzing errors in some theoretical case studies followed by other studies with real terrain elevation data. We also introduce and briefly present an iterative water routing method and use it for validation on a case with concrete terrain data.

cs.MS↗