Algorithms for solving Richards' equation for variably saturated soils

1992 ◽  
Vol 28 (8) ◽  
pp. 2049-2058 ◽  
Author(s):  
M. R. Kirkland ◽  
R. G. Hills ◽  
P. J. Wierenga
Keyword(s):  
Richards Equation ◽  
Saturated Soils

scholarly journals A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1604
Author(s):  
Carlos Chávez-Negrete ◽  
Daniel Santana-Quinteros ◽  
Francisco Domínguez-Mota
Keyword(s):  
Finite Differences ◽  
Test Problem ◽  
Soil Mechanics ◽  
Stationary Flow ◽  
Standard Test ◽  
Richards Equation ◽  
Saturated Soils ◽  
Transient Case ◽  
Comparative Results ◽  
Stationary Form

The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary.

SOLUTION OF THE RICHARDS EQUATION IN A SOIL PROFILE WITH TWO LAYERS USING THE METHOD OF LINES

2020 ◽  
Author(s):  
Diego Sousa Lopes ◽  
Augusto Cezar Cordeiro Jardim ◽  
Diego Estumano ◽  
Emanuel Macêdo ◽  
João Quaresma
Keyword(s):  
Soil Profile ◽  
Method Of Lines ◽  
Richards Equation ◽  
The Method Of Lines

Response of Saturated Soils to Dynamic Loading.

1984 ◽  
Author(s):  
R. S. Sandhu ◽  
S. J. Hong ◽  
B. L. Aboustit
Keyword(s):  
Dynamic Loading ◽  
Saturated Soils

A spatially and temporally adaptive solution of Richards’ equation

2006 ◽  
Vol 29 (4) ◽  
pp. 525-545 ◽  
Author(s):  
Cass T. Miller ◽  
Chandra Abhishek ◽  
Matthew W. Farthing
Keyword(s):  
Richards Equation ◽  
Adaptive Solution

Estimating and modelling the risk of redox-sensitive phosphorus loss from saturated soils using different soil tests

Geoderma ◽  
2021 ◽  
Vol 398 ◽  
pp. 115094
Author(s):  
G.J. Smith ◽  
R.W. McDowell ◽  
K. Daly ◽  
D. Ó hUallacháin ◽  
L.M. Condron ◽  
...  
Keyword(s):  
Saturated Soils ◽  
Soil Tests ◽  
Phosphorus Loss

scholarly journals Implicit and semi-implicit second-order time stepping methods for the Richards equation

2021 ◽  
Vol 148 ◽  
pp. 103841
Author(s):  
Sana Keita ◽  
Abdelaziz Beljadid ◽  
Yves Bourgault
Keyword(s):  
Second Order ◽  
Richards Equation ◽  
Time Stepping

scholarly journals Revisiting Surface-Subsurface Exchange at Intertidal Zone with a Coupled 2D Hydrodynamic and 3D Variably-Saturated Groundwater Model

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 902
Author(s):  
Zhi Li ◽  
Ben R. Hodges
Keyword(s):  
Intertidal Zone ◽  
Coastal Wetlands ◽  
High Performance ◽  
Stokes Equations ◽  
Wave Model ◽  
Surface Flow ◽  
Richards Equation ◽  
Navier Stokes ◽  
Dynamic Surface ◽  
Flow Equations

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.

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