TY - GEN
T1 - A Finite Difference Scheme for the Richards Equation Under Variable-Flux Boundary
AU - Fukumoto, Yasuhide
AU - Liu, Fengnan
AU - Zhao, Xiaopeng
N1 - Funding Information:
YF was supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (grant no. 19K03672), FL was supported by Fundamental Research Funds for Central Universities (no. DUT19RC(4)038), and XZ was supported by China Postdoctoral Science Foundation (no. 2015M581689).
Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
PY - 2021
Y1 - 2021
N2 - The Richards equation is a degenerate nonlinear partial differential equation which serves as a model for describing a flow of water through saturated/unsaturated porous medium under the action of gravity. This paper develops a numerical method, with a mathematical support, for the one-dimensional Richards equation. Implicit schemes based on a backward Euler format have been widely used, but have a difficulty in insuring the stability, because of the strong nonlinearity and degeneracy. A linearized semi-implicit finite difference scheme that is faster than the backward Euler implicit schemes is established, the stability of this scheme is proved by adding a small perturbation to the coefficient function, and an error estimate is made. It is found that there is a linear relationship between the discretization error in a certain norm and the perturbation strength.
AB - The Richards equation is a degenerate nonlinear partial differential equation which serves as a model for describing a flow of water through saturated/unsaturated porous medium under the action of gravity. This paper develops a numerical method, with a mathematical support, for the one-dimensional Richards equation. Implicit schemes based on a backward Euler format have been widely used, but have a difficulty in insuring the stability, because of the strong nonlinearity and degeneracy. A linearized semi-implicit finite difference scheme that is faster than the backward Euler implicit schemes is established, the stability of this scheme is proved by adding a small perturbation to the coefficient function, and an error estimate is made. It is found that there is a linear relationship between the discretization error in a certain norm and the perturbation strength.
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U2 - 10.1007/978-981-16-0077-7_22
DO - 10.1007/978-981-16-0077-7_22
M3 - Conference contribution
AN - SCOPUS:85104419403
SN - 9789811600760
T3 - Lecture Notes in Civil Engineering
SP - 231
EP - 245
BT - Advances in Sustainable Construction and Resource Management
A2 - Hazarika, Hemanta
A2 - Madabhushi, Gopal Santana
A2 - Yasuhara, Kazuya
A2 - Bergado, Dennes T.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 1st International Symposium on Construction Resources for Environmentally Sustainable Technologies, CREST 2020
Y2 - 9 March 2021 through 11 March 2021
ER -