scholarly journals Contribution to Numerical Modeling of Water Flow in Variably Saturated, Heterogeneous Porous Media

2015 ◽  
Vol 28 (3) ◽  
pp. 179-197 ◽  
Author(s):  
Adrien Wanko ◽  
Gabriela Tapia ◽  
Robert Mosé
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Water Flow ◽  
Numerical Test ◽  
Model Performance ◽  
Pressure Head ◽  
Soil Heterogeneity ◽  
Heterogeneous Porous Media ◽  
Richards Equation ◽  
Initial And Boundary Conditions

Abstract Solutions to the Richards equation for water flow in variably saturated porous media are the focus of this paper. Working with field conditions, the extreme variability and complexity of soil, initial and boundary conditions can make the flow problem difficult to solve. This paper proposes to improve the computational efficiency of the mixed hybrid finite element (MHFE) method coupled with the variables transformation. The transform variables were introduced in order to simulate problems with convergence difficulty attributed to the presence of sharp wetting fronts. Furthermore, for better convergence behaviour, a technique that switches between the mixed-form and the pressure-head based form of the Richard’s equation was applied. Special attention was given to the top boundary conditions dealing with ponding or evaporation problems. In order to avoid non-physical oscillation problems, a mass condensation scheme was implemented in the model. Performance indicators in time and error of different options of the numerical model are defined, analyzed and classified. Thus, for each test case, a suitable numerical method that identifies which form of the Richards equation is best suited, the relevance of the switching technique as well as the utility of the transformation of the primary variable is possible. The results for the 1D Numerical test cases that have been performed matched those from the literature results. For evaporation and infiltration problem’s, the number of iterations needed to get the solution decrease when using the method of transformed pressure. Finally, knowing the soil heterogeneity, initial and boundary conditions, an agglomerative hierarchical clustering allows to analyze the need or not to transform variables and to use other options.

scholarly journals Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 904
Author(s):  
Denis Spiridonov ◽  
Maria Vasilyeva ◽  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
Raghavendra Jana
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Surface Topography ◽  
Rough Surface ◽  
Heterogeneous Porous Media ◽  
Coarse Grid ◽  
Basis Functions ◽  
Richards Equation ◽  
Small Scale ◽  
Fine Grid

In this paper, we consider unsaturated filtration in heterogeneous porous media with rough surface topography. The surface topography plays an important role in determining the flow process and includes multiscale features. The mathematical model is based on the Richards’ equation with three different types of boundary conditions on the surface: Dirichlet, Neumann, and Robin boundary conditions. For coarse-grid discretization, the Generalized Multiscale Finite Element Method (GMsFEM) is used. Multiscale basis functions that incorporate small scale heterogeneities into the basis functions are constructed. To treat rough boundaries, we construct additional basis functions to take into account the influence of boundary conditions on rough surfaces. We present numerical results for two-dimensional and three-dimensional model problems. To verify the obtained results, we calculate relative errors between the multiscale and reference (fine-grid) solutions for different numbers of multiscale basis functions. We obtain a good agreement between fine-grid and coarse-grid solutions.

scholarly journals MEASUREMENT OF PREFERENTIAL FLOW DURING INFILTRATION AND EVAPORATION IN POROUS MEDIA

2017 ◽  
Vol 43 (4) ◽  
pp. 1831
Author(s):  
A. Papafotiou ◽  
C. Schütz ◽  
P. Lehmann ◽  
P. Vontobel ◽  
D. Or ◽  
...  
Keyword(s):  
Porous Media ◽  
Water Distribution ◽  
Preferential Flow ◽  
Unsaturated Flow ◽  
Coupling Effect ◽  
Heterogeneous Systems ◽  
Heterogeneous Porous Media ◽  
Richards Equation ◽  
Hydraulic Coupling ◽  
Experimental Findings

Infiltration and evaporation are governing processes for water exchange between soil and atmosphere. In addition to atmospheric supply or demand, infiltration and evaporation rates are controlled by the material properties of the subsurface and the interplay between capillary, viscous and gravitational forces. This is commonly modeled with semi-empirical approaches using continuum models, such as the Richards equation for unsaturated flow. However, preferential flow phenomena often occur, limiting or even entirely suspending the applicability of continuum-based models. During infiltration, unstable fingers may form in homogeneous or heterogeneous porous media. On the other hand, the evaporation process may be driven by the hydraulic coupling of materials with different hydraulic functions found in heterogeneous systems. To analyze such preferential flow processes, water distribution was monitored in infiltration and evaporation lab experiments using neutron transmission techniques. Measurements were performed in 2D and 3D, using homogeneous and heterogeneous setups. The experimental findings demonstrate the fingering effect in infiltration and how it is influenced by the presence of fine inclusions in coarse background material. During evaporation processes, the hydraulic coupling effect is found to control the evaporation rate, limiting the modeling of water balances between soil and surface based on surface information alone.

Vadose Zone, Part I : Characterization and Flow Processes

2003 ◽  
Author(s):  
Yoram Rubin
Keyword(s):  
Porous Media ◽  
Water Flow ◽  
Governing Equation ◽  
Vadose Zone ◽  
Stochastic Analysis ◽  
Transport Processes ◽  
Richards Equation ◽  
Saturated Porous Media ◽  
Flow And Transport ◽  
Flow Processes

Many of the principles guiding stochastic analysis of flow and transport processes in the vadose zone are those which we also employ in the saturated zone, and which we have explored in earlier chapters. However, there are important considerations and simplifications to be made, given the nature of the flow and of the governing equations, which we explore here and in chapter 12. The governing equation for water flow in variably saturated porous media at the smallest scale where Darcy’s law is applicable (i.e., no need for upscaling of parameters) is Richards’ equation (cf. Yeh, 1998)

scholarly journals Decadal evaluation of regional climate, air quality, and their interactions using WRF/Chem Version 3.6.1

2015 ◽  
Vol 8 (8) ◽  
pp. 6707-6756
Author(s):  
K. Yahya ◽  
K. Wang ◽  
P. Campbell ◽  
T. Glotfelty ◽  
J. He ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Global Analysis ◽  
Regional Climate ◽  
Model Performance ◽  
Cloud Droplet ◽  
Meteorological Variables ◽  
Cold Bias ◽  
Aerosol Cloud ◽  
Initial And Boundary Conditions

Abstract. The Weather Research and Forecasting model with Chemistry (WRF/Chem) v3.6.1 with the Carbon Bond 2005 (CB05) gas-phase mechanism is evaluated for its first decadal application during 2001–2010 using the Representative Concentration Pathway (RCP 8.5) emissions to assess its capability and appropriateness for long-term climatological simulations. The initial and boundary conditions are downscaled from the modified Community Earth System Model/Community Atmosphere Model (CESM/CAM5) v1.2.2. The meteorological initial and boundary conditions are bias-corrected using the National Center for Environmental Protection's Final (FNL) Operational Global Analysis data. Climatological evaluations are carried out for meteorological, chemical, and aerosol-cloud-radiation variables against data from surface networks and satellite retrievals. The model performs very well for the 2 m temperature (T2) for the 10 year period with only a small cold bias of −0.3 °C. Biases in other meteorological variables including relative humidity at 2 m, wind speed at 10 m, and precipitation tend to be site- and season-specific; however, with the exception of T2, consistent annual biases exist for most of the years from 2001 to 2010. Ozone mixing ratios are slightly overpredicted at both urban and rural locations but underpredicted at rural locations. PM2.5 concentrations are slightly overpredicted at rural sites, but slightly underpredicted at urban/suburban sites. In general, the model performs relatively well for chemical and meteorological variables, and not as well for aerosol-cloud-radiation variables. Cloud-aerosol variables including aerosol optical depth, cloud water path, cloud optical thickness, and cloud droplet number concentration are generally underpredicted on average across the continental US. Overpredictions of several cloud variables over eastern US result in underpredictions of radiation variables and overpredictions of shortwave and longwave cloud forcing which are important climate variables. While the current performance is deemed to be acceptable, improvements to the bias-correction method for CESM downscaling and the model parameterizations of cloud dynamics and thermodynamics, as well as aerosol-cloud interactions can potentially improve model performance for long-term climate simulations.

scholarly journals Numerical Evaluation of Fractional Vertical Soil Water Flow Equations

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 511
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Porous Media ◽  
Soil Water ◽  
Water Flow ◽  
Water Movement ◽  
Least Square ◽  
Flow In Porous Media ◽  
Fickian Diffusion ◽  
Richards Equation ◽  
Governing Equations ◽  
Soil Water Flow

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores the features of natural soils which are heterogeneous. Within this framework, governing equations of transient water flow in porous media in fractional time and multi-dimensional fractional soil space in anisotropic media were recently introduced by the authors by coupling Brooks–Corey constitutive relationships with the fractional continuity and motion equations. In this study, instead of utilizing Brooks–Corey relationships, empirical expressions, obtained by least square fits through hydraulic measurements, were utilized to show the suitability of the proposed fractional approach with other constitutive hydraulic relations in the literature. Next, a finite difference numerical method was proposed to solve the fractional governing equations. The applicability of the proposed fractional governing equations was investigated numerically in comparison to their conventional counterparts. In practice, cumulative infiltration values are observed to deviate from conventional infiltration approximation, or the wetting front through time may not be consistent with the traditional estimates of Richards equation. In such cases, fractional governing equations may be a better alternative for mimicking the physical process as they can capture sub-, super-, and normal-diffusive soil water flow processes during infiltration.

scholarly journals Decadal evaluation of regional climate, air quality, and their interactions over the continental US and their interactions using WRF/Chem version 3.6.1

2016 ◽  
Vol 9 (2) ◽  
pp. 671-695 ◽  
Author(s):  
Khairunnisa Yahya ◽  
Kai Wang ◽  
Patrick Campbell ◽  
Timothy Glotfelty ◽  
Jian He ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Global Analysis ◽  
Model Performance ◽  
Cloud Droplet ◽  
Meteorological Variables ◽  
Shortwave Radiation ◽  
Cold Bias ◽  
Aerosol Cloud ◽  
Initial And Boundary Conditions

Abstract. The Weather Research and Forecasting model with Chemistry (WRF/Chem) v3.6.1 with the Carbon Bond 2005 (CB05) gas-phase mechanism is evaluated for its first decadal application during 2001–2010 using the Representative Concentration Pathway 8.5 (RCP 8.5) emissions to assess its capability and appropriateness for long-term climatological simulations. The initial and boundary conditions are downscaled from the modified Community Earth System Model/Community Atmosphere Model (CESM/CAM5) v1.2.2. The meteorological initial and boundary conditions are bias-corrected using the National Center for Environmental Protection's Final (FNL) Operational Global Analysis data. Climatological evaluations are carried out for meteorological, chemical, and aerosol–cloud–radiation variables against data from surface networks and satellite retrievals. The model performs very well for the 2 m temperature (T2) for the 10-year period, with only a small cold bias of −0.3 °C. Biases in other meteorological variables including relative humidity at 2 m, wind speed at 10 m, and precipitation tend to be site- and season-specific; however, with the exception of T2, consistent annual biases exist for most of the years from 2001 to 2010. Ozone mixing ratios are slightly overpredicted at both urban and rural locations with a normalized mean bias (NMB) of 9.7 % but underpredicted at rural locations with an NMB of −8.8 %. PM2.5 concentrations are moderately overpredicted with an NMB of 23.3 % at rural sites but slightly underpredicted with an NMB of −10.8 % at urban/suburban sites. In general, the model performs relatively well for chemical and meteorological variables, and not as well for aerosol–cloud–radiation variables. Cloud-aerosol variables including aerosol optical depth, cloud water path, cloud optical thickness, and cloud droplet number concentration are generally underpredicted on average across the continental US. Overpredictions of several cloud variables over the eastern US result in underpredictions of radiation variables (such as net shortwave radiation – GSW – with a mean bias – MB – of −5.7 W m−2) and overpredictions of shortwave and longwave cloud forcing (MBs of  ∼  7 to 8 W m−2), which are important climate variables. While the current performance is deemed to be acceptable, improvements to the bias-correction method for CESM downscaling and the model parameterizations of cloud dynamics and thermodynamics, as well as aerosol–cloud interactions, can potentially improve model performance for long-term climate simulations.

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