A mixed MoL-TMoL for the numerical solution of the 2D Richards' equation in layered soils

被引：30
作者：
Berardi, Marco [1 ]
Difonzo, Fabio [2 ]
Lopez, Luciano [1 ,3 ]
机构：
[1] CNR, Ist Ric Acque, Via Blasio 5, I-70132 Bari, Italy
[2] Code Architects Automat, Via Campania 1, I-70029 Santeramo In Colle, Italy
[3] Univ Bari Aldo Moro, Dipartimento Matemat, Via Orabona 4, I-70125 Bari, Italy
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 79卷 / 07期
关键词：
Richards' equation; Layered soils; Discontinuous differential systems; Transversal method of lines; EVENT LOCATION TECHNIQUES; TRANSVERSAL METHOD; LINES TRANSPOSE; INFILTRATION; SYSTEMS; MODEL;
D O I：
10.1016/j.camwa.2019.07.026
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Water infiltration into layered soils is studied, considering a two dimensional spatial domain. The focus is on the treatment of discontinuity at the intersection of non-overlapping soils. The novelty of this paper is based on a mixed MoL-TMoL, which merges desirable features of both Method of Lines (MoL) and Transversal Method of Lines (TMoL): such a numerical approach allows us the numerical treatment of the solution at the discontinuous interfaces by means of Filippov theory for dynamical systems. Numerical simulations, based on implicit and semi-implicit schemes of low accuracy, are provided for validating this approach. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1990 / 2001
页数：12
相关论文
共 50 条
[1]   A numerical procedure for geochemical compaction in the presence of discontinuous reactions [J].
Agosti, Abramo ;
Giovanardi, Bianca ;
Formaggia, Luca ;
Scotti, Anna .
ADVANCES IN WATER RESOURCES, 2016, 94 :332-344
[2]  
[Anonymous], 1988, Differential Equations With Discontinuous Right-Hand Side
[3]   Strong solutions for Richards' equation with Cauchy conditions and constant pressure gradient [J].
Berardi, Marco ;
Difonzo, Fabio V. .
ENVIRONMENTAL FLUID MECHANICS, 2020, 20 (01) :165-174
[4]   A transversal method of lines for the numerical modeling of vertical infiltration into the vadose zone [J].
Berardi, Marco ;
Difonzo, Fabio ;
Notarnicola, Filippo ;
Vurro, Michele .
APPLIED NUMERICAL MATHEMATICS, 2019, 135 :264-275
[5]   The 1D Richards' equation in two layered soils: a Filippov approach to treat discontinuities [J].
Berardi, Marco ;
Difonzo, Fabio ;
Vurro, Michele ;
Lopez, Luciano .
ADVANCES IN WATER RESOURCES, 2018, 115 :264-272
[6]  
Berardi M, 2016, MEDITERR J MATH, V13, P4829, DOI 10.1007/s00009-016-0778-5
[7]   A new data assimilation technique based on ensemble Kalman filter and Brownian bridges: An application to Richards' equation [J].
Berardi, Marco ;
Andrisani, Andrea ;
Lopez, Luciano ;
Vurro, Michele .
COMPUTER PHYSICS COMMUNICATIONS, 2016, 208 :43-53
[8]   The numerical solution of Richards' equation by means of method of lines and ensemble Kalman filter [J].
Berardi, Marco ;
Vurro, Michele .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2016, 125 :38-47
[9]   Rosenbrock-type methods applied to discontinuous differential systems [J].
Berardi, Marco .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2014, 95 :229-243
[10]   On the continuous extension of Adams-Bashforth methods and the event location in discontinuous ODEs [J].
Berardi, Marco ;
Lopez, Luciano .
APPLIED MATHEMATICS LETTERS, 2012, 25 (06) :995-999
12345