scholarly journals Handling the water content discontinuity at the interface between layered soils within a numerical scheme

Soil Research ◽  
2005 ◽  
Vol 43 (8) ◽  
pp. 945 ◽  
Author(s):  
C. J. Matthews ◽  
F. J. Cook ◽  
J. H. Knight ◽  
R. D. Braddock
Keyword(s):  
Numerical Solution ◽  
Water Content ◽  
Numerical Scheme ◽  
Iterative Scheme ◽  
Method Of Lines ◽  
Soil Layer ◽  
Iterative Solution ◽  
Richards Equation ◽  
Layered Soils ◽  
Fine Soil

In general, the water content (θ) form of Richards’ equation is not used when modeling water flow through layered soil since θ is discontinuous across soil layers. Within the literature, there have been some examples of models developed for layered soils using the θ-form of Richards’ equation. However, these models usually rely on an approximation of the discontinuity at the soil layer interface. For the first time, we will develop an iterative scheme based on Newton’s method, to explicitly solve for θ at the interface between 2 soils within a numerical scheme. The numerical scheme used here is the Method of Lines (MoL); however, the principles of the iterative solution could be used in other numerical techniques. It will be shown that the iterative scheme is highly effective, converging within 1 to 2 iterations. To ensure the convergence behaviour holds, the numerical scheme will be tested on a fine-over-coarse and a coarse-over-fine soil with highly contrasting soil properties. For each case, the contrast between the soil types will be controlled artificially to extend and decrease the extent of the θ discontinuity. In addition, the numerical solution will be compared against a steady-state analytical solution and a numerical solution from the literature.

Modelling non-equillibrium unsaturated flow in soils during sudden pressure head changes by solving Richards' equation with a Method of lines approach

2021 ◽  
Author(s):  
Robert Mietrach ◽  
Thomas Wöhling ◽  
Niels Schütze
Keyword(s):  
Water Content ◽  
Preferential Flow ◽  
Unsaturated Flow ◽  
Full Range ◽  
Method Of Lines ◽  
Pressure Head ◽  
Richards Equation ◽  
Extended Model ◽  
Solution Methods ◽  
Numerical Robustness

<p>The classical formulation of Richards' equation is relying on a unique functional relationship between water content, conductivity and pressure head. Some phenomena like hystersis effects in the water content during wetting and drying cycles and hydraulic non-equillibrium cannot be accounted for with this formulation. Therefor it has been extended in different ways in the past to be able to include these effects in the simulation. Each modification comes with its own challenges regarding implementation and numerical stability.<br>The Method Of Lines approach to solving the Richards' equation has already be shown to be an efficient and stable alternative to established solution methods, such as low-order finite difference and finite element methods applied to the mixed form of Richards' equation.<br>In this work a slightly modified Method Of Lines approach is used to solve the pressure based 1D Richards' equation. A finite differencing scheme is applied to the spatial derivative and the resulting system of ordinary differential equations is reformulated as differential-algebraic system of equations. The open-source code IDAS from the Sundials suite is used to solve the DAE system. Different extensions to Richards' equation have been incorporated into the model to address the shortcomings mentioned above. These extensions are a model able to simulate preferential flow using a coupled two domain approach, a simple hysteretic model to account for hysteresis in the water retention curve and also two models to either fully or partially calculate hydraulic non-equillibrium effects. To verify the numerical robustness of the extended model, stochastic parameterizations were generated that represent the full range of all soil types. Simulations were carried out using these parameter sets and real-world meteorological boundary conditions at 10 minutes time intervals, that exhibit drastic flux changes and poses numerical challenges for classical solution methods.</p><p>The results show that not only does the extended model converge for all parameterizations, but that numerical robustness and performance is maintained. Where applicable the results have been verified against solutions from the software Hydrus and show good agreement with those.</p>

scholarly journals A Modified Green-Ampt Model and Parameter Determination for Water Infiltration in Fine-textured Soil with Coarse Interlayer

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 787
Author(s):  
Shuai Chen ◽  
Xiaomin Mao ◽  
Chunying Wang
Keyword(s):  
Water Content ◽  
Soil Column ◽  
Soil Layer ◽  
Water Infiltration ◽  
Richards Equation ◽  
Parameter Determination ◽  
Wetting Front ◽  
Soil Matrix ◽  
Simulation Results ◽  
Two Parameters

A modified Green-Ampt model was developed to simulate water infiltration in fine-textured soil with a coarse interlayer. Because under such a soil structure, the two soils may not be fully saturated during infiltration, the model introduced two parameters—that is, the saturation coefficients a and b, to reflect the incomplete saturation condition and their influence on infiltration processes. In order to analyze the variation pattern of the two parameters in the above proposed model, scenarios were set for soil column infiltration in fine-textured soil with a coarse interlayer under different buried depths. A Richards equation-based model (RE-Model) was built for simulating the above scenarios and to obtain the evolution of soil water content along the soil profiles. Simulation results show that the infiltration rate decreased to a constant value when the wetting front crossed the upper interface between the fine and coarse soil layer. The soil matrix suction (ψ2) at the upper interface remained unchanged after the wetting front advanced into the coarse layer, and the steady value of ψ2 showed a linear relationship with the buried depth of the coarse layer. Based on the simulation results of the RE-Model, a method was proposed to determine the saturation coefficients related to the relative hydraulic conductivity and water content at ψ2 in the modified Green-Ampt model. Then, the modified model was tested under various infiltration conditions with different soil layered structures, and the results showed good agreement with the experimental data.

scholarly journals A modification of the mixed form of Richards equation and its application in vertically inhomogeneous soils

2011 ◽  
Vol 6 (1) ◽  
pp. 123-127 ◽  
Author(s):  
F. Kalinka ◽  
B. Ahrens
Keyword(s):  
Water Content ◽  
Soil Water ◽  
Richards Equation ◽  
Soil Matric Potential ◽  
Water Fluxes ◽  
Layered Soils ◽  
Matric Potential ◽  
Soil Matrix ◽  
Matrix Potential ◽  
Modified Equation

Abstract. Recently, new soil data maps were developed, which include vertical soil properties like soil type. Implementing those into a multilayer Soil-Vegetation-Atmosphere-Transfer (SVAT) scheme, discontinuities in the water content occur at the interface between dissimilar soils. Therefore, care must be taken in solving the Richards equation for calculating vertical soil water fluxes. We solve a modified form of the mixed (soil water and soil matric potential based) Richards equation by subtracting the equilibrium state of soil matrix potential ψE from the hydraulic potential ψh. The sensitivity of the modified equation is tested under idealized conditions. The paper will show that the modified equation can handle with discontinuities in soil water content at the interface of layered soils.

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
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