An effective numerical method for solving the Richards-Klute equation with tracking of full saturated zone
DOI:
https://doi.org/10.17721/1812-5409.2023/2.37Keywords:
mathematical modeling, numerical methods, computational optimization, Richards-Klute equation, doubly connected edge listAbstract
The article presents modifications for numerical methods for modeling of mass transfer process in porous medium with full saturated zone tracking. The goal of the article is to increase computational efficiency of finding an approximate solution process using division of the area into the two non-intersecting parts: unsaturated zone and zone with full saturation. Numerical methods for solving the one-dimensional Richards-Klute equation with tracking of the full saturated zone have been developed. The cases of monotonic solution and solution with general properties of Richards-Klute equation were considered. A modification of the full saturated zone tracking process using a doubly connected edge list structure have been developed for two-dimensional case. Efficiency increase estimation is proven for one- and two-dimensional cases using probability distibution for a measure of the full saturated zone. A comparative analysis of the proposed modifications was carried out. The results of numerical experiments coincide with the estimates predicted by theory.
Pages of the article in the issue: 206 - 213
Language of the article: Ukrainian
References
SRIVASTAVA, R., JIM YEH, T.-C. (1991) Analytical Solutions for One-Dimensional, Transient Infiltration Toward the Water Table in Homogeneous and Layered Soil. Water Resources Research. 27 (5). p.753–762. https://doi.org/10.1029/90WR02772
BROADBRIDGE, P., DALY, E., GOARD, J. (2017) Exact Solutions of the Richards Equation With Nonlinear Plant-Root Extraction. Water Resources Research. 53. p.9679–9691. https://doi.org/10.1002/2017WR021097
De LUCA, D.L., CEPEDA, J.M. (2016) Procedure to Obtain Analytical Solutions of One-Dimensional Richards’ Equation for Infiltration in Two-Layered Soils. Journal of Hydrologic Engineering. 21 (7). https://doi.org/10.1061/(ASCE)HE.1943- 5584.0001356
ALT, H. W., LUCKHAUS, S. (1983) Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1). p.311–341. https://doi.org/10.1007/BF01176474
BERTSCH, M., HULSHOF, J. (1986) Regularity Results for an Elliptic-Parabolic Free Boundary Problem. Transactions of the American Mathematical Society. 297 (1). p.337–350. https://doi.org/10.2307/2000472
SOLIN, P., KURAZ, M. (2011) Solving the nonstationary Richards equation with adaptive hp-FEM. Advances in Water Resources. 34 (9). p.1062–1081. https://doi.org/10.1016/j.advwatres.2011.04.020
KOLESNYKOV, V.A. (2023) Analysis of the construction of numerical methods for solving the Richards-Klute equation. J. Num. Appl. Math. 1. p.28–38. https://doi.org/10.17721/2706-9699.2023.1.03
CELIA, M., BOULOUTAS, E., ZABRA, R. (1990) A general mass-conservative numerical solution for the unsaturated flow equation. Water Resources Research. 26 (1). p.1483–1496. https://doi.org/10.1007/11823285_121
FARTHING, M.W., OGDEN, F.L. (2017) Numerical Solution of Richards’ Equation: A Review of Advances and Challenges. Soil Science Society of America Journal. 81 (6). p.1257–1269. https://doi.org/10.2136/sssaj2017.02.0058
ZHA, Y., YANG, J., ZENG, J., TSO, C.-H. M., ZENG, W., SHI, L. (2019) Review of numerical solution of Richardson-Richards equation for variably saturated flow in soils. WIREs Water. 6 (5). https://doi.org/10.1002/wat2.1364
DEGTYAREV, S. P. (2014) Elliptic-parabolic equation and the corresponding free boundary problem I: Elliptic problem with a parameter. Ukr. Math. Vystnyk. 11 (1). p.15–48.
DEGTYAREV, S. P. (2014) Elliptic-parabolic equation and the corresponding free boundary problem II: smooth solution. Ukr. Math. Vystnyk. 11 (1). p.447–479.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 V. A. Kolesnykov
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
