Two-dimensional Subsurface Flow Research Articles

Analytical solutions for solute transport in groundwater and riverine flow using Green’s Function Method and pertinent coordinate transformation method

In this study, analytical solutions of one-dimensional pollutant transport originating from instantaneous and continuous point sources were developed in groundwater and riverine flow using both Green’s Function Method (GFM) and pertinent coordinate transformation method. Dispersion coefficient and flow velocity are considered spatially and temporally dependent. The spatial dependence of the velocity is linear, non-homogeneous and that of dispersion coefficient is square of that of velocity, while the temporal dependence is considered linear, exponentially and asymptotically decelerating and accelerating.Our proposed analytical solutions are derived for three different situations depending on variations of dispersion coefficient and velocity, respectively which can represent real physical processes occurring in groundwater and riverine systems. First case refers to steady solute transport situation in steady flow in which dispersion coefficient and velocity are only spatially dependent. The second case represents transient solute transport in steady flow in which dispersion coefficient is spatially and temporally dependent while the velocity is spatially dependent. Finally, the third case indicates transient solute transport in unsteady flow in which both dispersion coefficient and velocity are spatially and temporally dependent. The present paper demonstrates the concentration distribution behavior from a point source in realistically occurring flow domains of hydrological systems including groundwater and riverine water in which the dispersivity of pollutant’s mass is affected by heterogeneity of the medium as well as by other factors like velocity fluctuations, while velocity is influenced by water table slope and recharge rate. Such capabilities give the proposed method’s superiority about application of various hydrological problems to be solved over other previously existing analytical solutions. Especially, to author’s knowledge, any other solution doesn’t exist for both spatially and temporally variations of dispersion coefficient and velocity.In this study, the existing analytical solutions from previous widely known studies are used for comparison as validation tools to verify the proposed analytical solution as well as the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) code and the developed 1D finite difference code (FDM). All such solutions show perfect match with the respective proposed solutions.

Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients

This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species’ concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push–pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.

A surface and subsurface model for the simulation of rainfall infiltration in slopes

Rainfall infiltration is one of the major triggering factors leading to slope failures in geotechnical engineering. Numerical investigation on rainfall infiltration is often based on Richards’ equation, which ignores the surface water effects and simplifies the boundary conditions. In reality, rainfall, infiltration, and surface runoff are interacted simultaneously. In this paper a new conjunctive one-dimensional surface flow and two-dimensional subsurface flow model for geotechnical slope is developed. The interaction between surface and subsurface flow is the interface infiltration rate, which is obtained by iterations. The results of comparisons between coupled and uncoupled models show that the surface water depth rises up as runoff increases and it tends to a dynamic balance state with a steady surface water depth. Interaction between surface and subsurface flow has remarkable effects on infiltration process. According to the results of coupled model, more rainwaters infiltrate into the slope. Therefore, pore water pressure changes faster and the wetting front moves deeper into the soil. Under initial drier condition, the capacity of infiltration is higher and more rainfall can be absorbed into slope, thus the differences of infiltration rate and pore water pressure between the coupled and uncoupled model are more significant.

Physically Based Coupled Model for Simulating 1D Surface–2D Subsurface Flow and Plant Water Uptake in Irrigation Furrows. I: Model Development

Physically based modeling of the interacting water flow during a furrow irrigation season can contribute to both a sustainable irrigation management and an improvement of the furrow irrigation efficiency. This paper presents a process based seasonal furrow irrigation model which describes the interacting one-dimensional surface — two-dimensional subsurface flow and crop growth during a whole growing period. The irrigation advance model presented in a previous study is extended to all hydraulic phases of an irrigation event. It is based on an analytical solution of the zero-inertia surface flow equations and is iteratively coupled with the two-dimensional subsurface flow model HYDRUS-2. A conceptual crop growth model calculates daily evaporation, transpiration and leaf area index. The crop model and HYDRUS-2 are coupled via its common boundaries, namely (1) by the flux across the soil-atmosphere interface; and (2) by the flux from the root zone, which is associated with the plant water uptake. We assume the water stress is the only environmental factor reducing crop development and hence final crop yield. The model performance is evaluated with field experimental data in the companion paper, Part II: Model Test and Evaluation (Wohling and Mailhol 2007).

Physically Based Coupled Model for Simulating 1D Surface–2D Subsurface Flow and Plant Water Uptake in Irrigation Furrows. II: Model Test and Evaluation

A physically based seasonal Furrow Irrigation Model was developed, which comprises three modules: The one-dimensional surface flow, the two-dimensional subsurface flow, and a crop model. The modeling principles of these modules, their simultaneous coupling, and the solution strategies were described in a companion paper (Wöhling and Schmitz 2007). In the current contribution, we present the model testing with experimental data from five real-scale laboratory experiments [Hubert-Engels Laboratory (HEL)], two field experiments in Kharagpur, Eastern India (KGP), one literature data set [Flowell-wheel (FW)], and data from three irrigations during a corn growing season in Montpellier, Southern France [Lavalette experiments (LAT)]. The simulated irrigation advance times match well with the observations of the HEL, FW, and KGP experiments, which is confirmed by coefficients of determination R2⩾0.99 and coefficients of efficiency Ce⩾0.7. Predicted recession times also match with the observations of the HEL runs, however, the values of R2⩾0.9 and Ce⩾0.6 are lower for predicted recession times as compared to predicted advance times. In contrast to the other experiments in the study, advance times are underpredicted for the experiments in France. The established soil hydraulic parameters for this site lead to an underestimation of the actual initial infiltration capability of the soil. In the long-term simulation, however, the overall change in soil moisture storage is correctly predicted by the model and the calculated yield of 12.8tha−1 is in very good agreement with the observations (12.7tha−1). We evaluated the sensitivity of the input parameters with regards to predicted advance time and runoff in both a 26.4m long furrow and a long 360m long furrow. The analysis revealed that calculated runoff is four to five times more sensitive to the inlet flow rate than to infiltration parameters. Furrow geometry parameters are most sensitive to calculated advance times in the short furrow with low infiltration opportunity time, whereas the inflow rate and infiltration parameters are more sensitive to calculated advance times in the long furrow with larger infiltration opportunity time.

Efficient Solution of the Coupled One-Dimensional Surface—Two-Dimensional Subsurface Flow during Furrow Irrigation Advance

Physically based modeling of the coupled one-dimensional surface and two-dimensional (2D) subsurface flow during furrow irrigation advance often causes numerical instabilities and nonconvergence problems. This is particularly the case for low irrigation advance rates when infiltration consumes a predominant part of the inflow volume. The proposed furrow advance phase model (FAPS) further develops the concepts of a previous study. An analytical zero-inertia surface flow model is iteratively coupled with the 2D subsurface water transport model HYDRUS-2. In contrast to the previous study, the flow domain is discretized using fixed space increments and the resulting set of nonlinear flow equations is solved using the Newton method. The complexity of the model was reduced by process adequate simplifications. FAPS exhibited better convergence, numerical stability, and less computational time than the original fixed time interval solution. The new solution converged rapidly for a number of model tests with various inflow rates including runs with very slow irrigation advance. Simulation model predictions agree very well with advance times measured in laboratory and field tests.

Finite Analytic Model for Flow and Transport in Unsaturated Zone

The finite analytic method is employed to solve the vertical, two-dimensional subsurface flow and transport equations in an unsaturated zone. The finite analytic method treats the nonlinear coefficient terms of the governing equations as constants in the element so that linearized partial differential equations can be obtained and solved in each element. The accuracy and limitations of the numerical method are systematically explored. The flow and transport simulations are examined using a one-dimensional laboratory infiltration test and an analytical solution of a two-dimensional subsurface transport problem, respectively. In the advection-dominant, vertical, one-dimensional infiltration problem, nine spatial weighting schemes are proposed to evaluate the averaged unsaturated hydraulic conductivity in a discretized element. Among them, the geometric mean weighting scheme provides the most accurate results as compared with the infiltration data. In verification of the two-dimensional solute transport problem, the nine-node elements are placed in the interior domain, and different layers of five-node elements are placed at the boundaries to investigate if the numerical experiment setup was proper and the algorithm was accurate. The developed numerical model is then applied to an irregular-domain landfill leaching problem to reveal the features of subsurface transport in unsaturated zone. Numerical aspects to be further explored are suggested.