The 1D Richards’ equation in two layered soils: a Filippov approach to treat discontinuities

Berardi, Marco; Difonzo, Fabio V.; Vurro, Michele; Lopez, L.

doi:10.1016/j.advwatres.2017.09.027

Cited by 35 publications

(18 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Whereas the surfactant transport is described by a reaction-diffusion-convection equation, water flow in variably saturated porous media is modelled by the Richards equation [7,18]. The main assumption in this case is that the air remains in contact with the atmosphere, having a constant pressure (the atmospheric pressure, here assumed zero).…”

Section: Introductionmentioning

confidence: 99%

Iterative schemes for surfactant transport in porous media

2020

View full text Add to dashboard Cite

In this work, we consider the transport of a surfactant in variably saturated porous media. The water flow is modelled by the Richards equations and it is fully coupled with the transport equation for the surfactant. Three linearization techniques are discussed: the Newton method, the modified Picard, and the L-scheme. Based on these, monolithic and splitting schemes are proposed and their convergence is analyzed. The performance of these schemes is illustrated on five numerical examples. For these examples, the number of iterations and the condition numbers of the linear systems emerging in each iteration are presented.

show abstract

Section: Introductionmentioning

confidence: 99%

Iterative schemes for surfactant transport in porous media

2020

View full text Add to dashboard Cite

show abstract

“…With TMoL, a system of second‐order differential equations in the space variable is derived as an initial value problem (Berardi, Difonzo, Notarnicola, & Vurro, ) by imposing both pressure head and its gradient at the top of the soil column. The proposed method has been proven to be cost‐effective for simulating infiltration problems, and it also has the benefit to handling the discontinuity of RRE well when heterogeneity of soil is present (Berardi et al, ).…”

Section: Spatial and Temporal Discretizationmentioning

confidence: 99%

“…Filippov approach is a widely used method for handling discontinuity in differential systems. By replacing the bottom boundary condition with a surface gradient condition, Berardi, Difonzo, Vurro, and Lopez () introduced the Filippov approach to handle discontinuity issue of RRE for a two‐layered soil, in which the numerical equation at each time is an initial value problem described by a second‐order differential system in space variable, and it is solved by a predictor–corrector method. This is a promising approach and future work can be focused on extending it to two‐ or three‐dimensional problems.…”

Section: Spatial and Temporal Discretizationmentioning

confidence: 99%

Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

et al. 2019

View full text Add to dashboard Cite

Modeling variably saturated flow in the vadose zone is of vital importance to many scientific fields and engineering applications. Richardson-Richards equation (RRE, which is conventionally known as Richards' equation) is often chosen to physically represent the fluxes in the vadose zone when the accurate characterization of the soil water dynamics is required. Being a highly nonlinear partial differential equation, RRE is often solved numerically. Although there are mature software and codes available for simulating variably saturated flow by solving RRE, the numerical solution of RRE is nevertheless computationally expensive.Moreover, sometimes the robustness and the efficiency of RRE-based models can deteriorate rapidly when certain unfavorable conditions are met. These demerits of RRE hinder its application on large-scale vadose zone hydrology problems and uncertainty quantification, both of which requires many runs of the prediction model. To address these challenges, the accuracy, convergence, and efficiency of the numerical schemes of RRE should be further improved by testing a wide variety of cases covering different initial conditions, boundary conditions, and soil types. We reviewed and highlighted several critical issues related to the numerical modeling of RRE, including spatial and temporal discretization, the different forms of RREs, iterative and noniterative schemes, benchmark solutions, and available software and codes. Based on the review, we summarize the challenges and future work for solving RRE numerically.

show abstract

“…Spatial geological heterogeneity often characterizes the subsurface medium of the alluvial plain [30]. The water infiltration in both the unsaturated and saturated zone with heterogenous properties is a complex process [31][32][33][34]. The heterogenous subsurface medium could offer a preferential flow path for surface water recharge to the aquifer [35].…”

Section: Introductionmentioning

confidence: 99%

Variations of Groundwater Dynamics in Alluvial Aquifers with Reclaimed Water Restoring the Overlying River, Beijing, China

Zhu

Han

Song

et al. 2021

Water

View full text Add to dashboard Cite

Some of the rivers in northern China are dried, and reclaimed water (RW) is used to restore these degraded river ecosystems, during which the RW could recharge the aquifer by river bank infiltration. From 2007 to 2018, 2.78 × 108 m3 of RW has been replenished to the dried Chaobai River (Shunyi reach), Beijing, China, which is located on the edge of one depression cone in groundwater caused by groundwater over-pumping. The groundwater hydrodynamic variations and the flow path of the RW were identified by eight-year hydrological, hydrochemical, and stable isotopic data, together with multivariate statistical analysis. The RW infiltration drastically impacts the groundwater dynamics with a spatiotemporal variation. The 30-m depth groundwater levels at Perennial intake reach increased quickly around 3 m after 2007, which indicated that they were dominated by RW infiltration. Other 30-m depth groundwater levels were controlled by precipitation recharge from 2007 to 2011, showing significant seasonal variations. In 2012, with more RW transferred to the river, the hydrodynamic impact of the RW on 30-m depth aquifer expanded downstream. However, the 50-m and 80-m depth groundwater levels showed decreasing trend with seasonal variations, due to groundwater pumping. The 30-m depth aquifer was mainly recharged by RW, being evidenced by the enriched δ2H and δ18O. The depleted δ2H and δ18O of the 50-m and 80-m depth groundwater indicated that they were dominated by regional groundwater with meteoric origin. The heterogenous properties of the multi-layer alluvial aquifer offer the preferential flow path for RW transport in the aquifers. The proportion of the RW in the aquifers decreases with depth that was calculated by the chloride conservative mixing model. The increased lateral hydraulic gradient (0.43%) contributes to the RW transport in the 30-m depth aquifer. RW usage changed 30-m depth groundwater type from Ca·Mg-HCO3 to Na·Ca·Mg-HCO3·Cl. RW preferentially recharged the 50-m and 80-m depth aquifers by vertical leakage.

show abstract

The 1D Richards’ equation in two layered soils: a Filippov approach to treat discontinuities

Cited by 35 publications

References 43 publications

Iterative schemes for surfactant transport in porous media

Iterative schemes for surfactant transport in porous media

Review of numerical solution of Richardson–Richards equation for variably saturated flow in soils

Variations of Groundwater Dynamics in Alluvial Aquifers with Reclaimed Water Restoring the Overlying River, Beijing, China

Contact Info

Product

Resources

About