Numerical Identification of Boundary Conditions for Richards’ Equation-Reference-Cited by-同舟云学术

Numerical Identification of Boundary Conditions for Richards’ Equation

Published:2024-01-17 Issue:2 Volume:12 Page:299
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Koleva Miglena N.¹^ORCID,Vulkov Lubin G.²

Affiliation:

1. Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, Bulgaria

2. Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, Bulgaria

Abstract

A time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards’ equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D case, obtained after this semidiscretization, a finite volume method is used for direct problems arising on each time level. Next, we propose a version of the decomposition method for the numerical solution of the inverse ODE and 2D elliptic boundary problems. Computational results for some soil types and its related parameters reported in the literature are presented.

Funder

Bulgarian Science Fund

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/2/299/pdf

Reference50 articles.

1. On a numerical approxiamtion of highly non-linear parabolic inverse problem in hydrology;Chakib;Ann. Univ. Craiova, Math. Comput. Sci. Ser.,2015

2. Efficient uncertainty quantification techniques in inverse problems for Richards’ equation using coarse-scale simulation models;Dostert;Adv. Water Resour.,2009

3. On the construction of a functional solution method for the infiltration in porous media problems;Furtado;Phys. A Stat. Mech. Its Appl.,2016

4. Weighted time-semidiscretization quasilinearization method for solving Richards’ equation;Koleva;Lect. Notes Comput. Sci.,2020

5. Popova, Z., Crevoisier, D., Mailhol, J., and Ruelle, P. (2007, January 2–7). Assessment and simulation of water and nitrogen transfer under furrow irrigation: Application of hydrus 2D model to simulate nitrogen transfer. Proceedings of the ICID 22nd European Regional Conference 2007, Pavia, Italy.