An improved method for the calculation of unsaturated–saturated water flow by coupling the FEM and FDM

Gao, Yulong; Pu, Shengyan; Chen, Kewei; Yi, Shuping

doi:10.1038/s41598-019-51405-4

Cited by 18 publications

(11 citation statements)

References 26 publications

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“…Most of the multiphase/three-phase groundwater flow equation solvers employ either FDM or finite element method (FEM) in the three coordinate space. Hybrid combinations are also possible 9 . Other used methods are: transversal methods of lines for the numerical modeling of vertical infiltration into the vadose zone 28 , 29 , or a WENO based method of lines 30 .…”

Section: High Performance Computing and Cactushydromentioning

confidence: 99%

“…Because these equations are highly nonlinear, degenerate elliptic-parabolic PDEs 7 , with a possible dominating hyperbolic advection term (the effect of gravity), cannot be resolved analytically, except for very simplified one-dimensional cases 5 , 8 . Therefore, numerical approximations schemes such as Finite Difference Method (FDM), Finite Element Method (FEM), or mixed combinations 9 , among others, are used to simulate unsaturated–saturated flow models. Several methods were proposed to resolve convergence issues and reduce mass-balance errors 10 , 11 .…”

Section: Introductionmentioning

confidence: 99%

“…Several papers show results on numerical simulations for transient saturated-unsaturated water flow 4 , 12 – 15 . In 9 an improved method for treating the unsaturated zone and saturated water flow together, using an improved FDM and FEM mixed combination is presented. The horizontal direction of the governing equation is discretized using the FEM, while the FDM is used in the vertical direction.…”

Section: Introductionmentioning

confidence: 99%

“…CactusHydro is based on the Cactus computational toolkit 23 , an open-source software framework for developing parallel HPC simulation codes. We check our code’s validity with two analytical examples, the inviscid Burgers’ equation and the Buckley–Leverett model , and a 2D numerical unsaturated–saturated water flow model 9 together with the sand tank experimental data conducted in Ref. 24 (see Supplementary Information).…”

Section: Introductionmentioning

confidence: 99%

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High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

Feo

Celico

2021

Sci Rep

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Numerical modeling of immiscible contaminant fluid flow in unsaturated and saturated porous aquifers is of great importance in many scientific fields to properly manage groundwater resources. We present a high-resolution numerical model that simulates three-phase immiscible fluid flow in both unsaturated and saturated zone in a porous aquifer. We use coupled conserved mass equations for each phase and study the dynamics of a multiphase fluid flow as a function of saturation, capillary pressure, permeability, and porosity of the different phases, initial and boundary conditions. To deal with the sharp front originated from the partial differential equations’ nonlinearity and accurately propagate the sharp front of the fluid component, we use a high-resolution shock-capturing method to treat discontinuities due to capillary pressure and permeabilities that depend on the saturation of the three different phases. The main approach to the problem’s numerical solution is based on (full) explicit evolution of the discretized (in-space) variables. Since explicit methods require the time step to be sufficiently small, this condition is very restrictive, particularly for long-time integrations. With the increased computational speed and capacity of today’s multicore computer, it is possible to simulate in detail contaminants’ fate flow using high-performance computing.

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Section: High Performance Computing and Cactushydromentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

Feo

Celico

2021

Sci Rep

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“…The numerical methods-finite difference and finite element-presented in [20]- [33] overcome most of the limitations to result to analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Analytical Solution to Vertical Infiltration

Tzimopoulos¹,

Papaevangelou²,

Papadopoulos³

et al. 2020

JSEA

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In this article, we examine the solution of the fuzzy linear vertical infiltration equation, which represents the water movement in porous media in that part which is called the vadose zone. This zone is very important for semi-arid areas, due to complex phenomena related to the moisture content in it. These phenomena concern the interchange of moisture content between the vadose zone and the atmosphere, groundwater and vegetation, transfer of moisture and vapor and retention of moisture. The equation describing the problem is a partial differential parabolic equation of second order. The calculation of water flow in the unsaturated zone requires the knowledge of the initial and boundary conditions as well as the various soil parameters. But these parameters are subject to different kinds of uncertainty due to human and machine imprecision. For that reason, fuzzy set theory was used here for facing imprecision or vagueness. As the problem concerns fuzzy differential equations, the generalized Hukuhara (gH) derivative was used for total derivatives, as well as the extension of this theory for partial derivatives. The results are the fuzzy moisture content, the fuzzy cumulative infiltration and the fuzzy infiltration rate versus time. These results allow researchers and engineers involved in Irrigation and Drainage Engineering to take into account the uncertainties involved in infiltration.

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Dissecting changes in evapotranspiration and its components across the Losses Plateau of China during 2001–2020

Sun,

Ma,

Liu

et al. 2024

Intl Journal of Climatology

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China's Losses Plateau (LP) is one of the ecologically vulnerable and the most severe soil erosion regions. Thus, knowing spatiotemporal changes in evapotranspiration (ET) and its components (soil evaporation, E; transpiration, T; and vegetation interception evaporation, EI) and revealing the underlying mechanisms are vital for ecosystem and water resources sustainability for this region. Here, we investigate the spatiotemporal changes in ET and its components and then quantify the impacts of climate variables (i.e., precipitation, radiation, temperature, and relative humidity) and vegetation dynamics (e.g., land use/cover changes [LUCC] and changes in leaf area index [LAI]) on their annual trends, by using a process‐based terrestrial ecosystem model and a joint‐solution method with multiple sensitivity numerical experiments. Results show that over 67% of the study region experienced significant (p < 0.05) increases in annual ET, T, and EI, with regional average rises of 4.05, 3.67, and 0.74 mm·year−1, respectively. However, there are significant (p < 0.05) decreases in regional mean E of 0.38 mm·year−1, and the negative trend covers 35.8% of the study area. E, T, and EI changes dominate the annual ET trends over 11.8%, 87.3%, and 0.9% of the study area, respectively. Attribution analyses highlight the increased LAI as the critical factor governing these trends across most of the LP (>58%). At the same time, precipitation and LUCC play a more dominant role in the remaining areas. This study emphasizes the spatial heterogeneity in the drivers of changes in ET and its components and highlights the critical role of vegetation dynamics. These findings provide valuable insights for understanding the ET processes and guiding sustainable water resource management in the LP.

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An improved method for the calculation of unsaturated–saturated water flow by coupling the FEM and FDM

Cited by 18 publications

References 26 publications

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

Fuzzy Analytical Solution to Vertical Infiltration

Dissecting changes in evapotranspiration and its components across the Losses Plateau of China during 2001–2020

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