363 research outputs found

    NUMERICAL SIMULATION OF A SINGLE RING INFILTRATION EXPERIMENT WITH hp-ADAPTIVE SPACE-TIME DISCONTINUOUS GALERKIN METHOD

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    We present a novel hp-adaptive space-time discontinuous Galerkin (hp-STDG) method for the numerical solution of the nonstationary Richards equation equipped with Dirichlet, Neumann and seepage face boundary conditions. The hp-STDG method presented in this paper is a generalization of a hp-STDG method which was developed for time dependent non-linear convective-diffusive problems. We describe the method and the single ring experiment, and then we present a numerical experiment which clearly demonstrates the superiority of the hp-STDG method over a discontinuous Galerkin method based on a static fine mesh

    A linear domain decomposition method for partially saturated flow in porous media

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    The Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface Γ\Gamma. This leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at Γ\Gamma. After an Euler implicit discretisation of the resulting nonlinear subproblems a linear iterative (LL-type) domain decomposition scheme is proposed. The convergence of the scheme is proved rigorously. In the last part we present numerical results that are in line with the theoretical finding, in particular the unconditional convergence of the scheme. We further compare the scheme to other approaches not making use of a domain decomposition. Namely, we compare to a Newton and a Picard scheme. We show that the proposed scheme is more stable than the Newton scheme while remaining comparable in computational time, even if no parallelisation is being adopted. Finally we present a parametric study that can be used to optimize the proposed scheme.Comment: 34 pages, 13 figures, 7 table

    Developing a reliable strategy to infer the effective soil hydraulic properties from field evaporation experiments for agro-hydrological models

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    The Richards equation has been widely used for simulating soil water movement. However, the take-up of agro-hydrological models using the basic theory of soil water flow for optimizing irrigation, fertilizer and pesticide practices is still low. This is partly due to the difficulties in obtaining accurate values for soil hydraulic properties at a field scale. Here, we use an inverse technique to deduce the effective soil hydraulic properties, based on measuring the changes in the distribution of soil water with depth in a fallow field over a long period, subject to natural rainfall and evaporation using a robust micro Genetic Algorithm. A new optimized function was constructed from the soil water contents at different depths, and the soil water at field capacity. The deduced soil water retention curve was approximately parallel but higher than that derived from published pedo-tranfer functions for a given soil pressure head. The water contents calculated from the deduced soil hydraulic properties were in good agreement with the measured values. The reliability of the deduced soil hydraulic properties was tested in reproducing data measured from an independent experiment on the same soil cropped with leek. The calculation of root water uptake took account for both soil water potential and root density distribution. Results show that the predictions of soil water contents at various depths agree fairly well with the measurements, indicating that the inverse analysis is an effective and reliable approach to estimate soil hydraulic properties, and thus permits the simulation of soil water dynamics in both cropped and fallow soils in the field accurately

    Modeling multiphase flow in porous medium systems at multiple scales

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    Problems involving multiphase flow and transport in porous media arise in a number of scientific and engineering applications including oil reservoir engineering and groundwater remediation. The inherent complexity of multiphase systems and the marked heterogeneity over multiple spatial scales result in significant challenges to the fundamental understanding of the multiphase flow and transport processes. For many decades, multiphase flow has been modeled using the traditional approach based on mass conservation and the generalized Darcy's law. The traditional approach, however, is subject to model errors and numerical errors. The focus of this dissertation research is to improve models of flow and transport in porous medium systems using numerical modeling approaches for a range of scales including pore scale and continuum scale. A major part of this research examines the deficiency of Darcy's relationship and its extension to multiphase flow using the lattice-Boltzmann (LB) approach. This study investigates the conventional relative permeability saturation relation for systems consisting of water and non-aqueous phase liquid (NAPL). In addition, it also examines the generalized formulation accounting for the interfacial momentum transfer and lends additional support to the hypothesis that interfacial area is a critical variable in multiphase porous medium systems. Another major part of the research involves developing efficient and robust numerical techniques to improve the solution approach for existing models. In particular, a local discontinuous Galerkin (LDG) spatial discretization method is developed in combination with a robust and established variable order, variable step-size temporal integration approach to solve Richards' equation (RE). Effective spatial adaptive LDG methods are also developed to further enhance the efficiency. The resulting simulator with both spatial and temporal adaption has demonstrated good performance for a series of problems modeled by RE

    Deterministic and Random Isogeometric Analysis of Fluid Flow in Unsaturated Soils

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    The main objective of this research is to use IGA as an efficient and robust alternative for numerical simulation of unsaturated seepage problems. Moreover, this research develops an IGA-based probabilistic framework that can properly account for the variability of soil hydraulic properties in the simulations. In the first part, IGA is used in a deterministic framework to solve a head-based form of Richards’ equation. It is shown that IGA is able to properly simulate changes in pore pressure at the soils interface. In the second part of this research, a new probabilistic framework, named random IGA (RIGA), is developed. A joint lognormal distribution function is used with IGA to perform Monte Carlo simulations. The results depict the statistical outputs relating to seepage quantities and pore water pressure. It is shown that pore water pressure, flow rate, etc. change considerably with respect to standard deviation and correlation of the model parameters

    Nitrate movement under a ridge configuration: a field and model investigation

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    A substantial portion of the nitrogen (N) fertilizer applied under intensive Midwestern cropping is lost through nitrate-nitrogen (NO[subscript]3-N) leaching with percolating water. A tillage and fertilizer-placement system designed to isolate the fertilizer from downward water flow and to minimize NO[subscript]3-N leaching is desirable, both environmentally and economically. A ridge-tillage configuration, with placement of the potential NO[subscript]3-N source in the elevated portion of the ridge, appears to be one possible best management practice. Therefore, NO[subscript]3-N leaching under ridge tillage during the early growing season and immediately following fertilizer application is investigated;Past numerical modeling of water and solute transport for both saturated and unsaturated soil is reviewed. The finite element formulation for two-dimensional water and solute transport is presented. The FEMWATER-FEMWASTE computer code is used for simulation modeling and a comparison is made of the water and solute transport in ridge- and flat-tillage systems;Data from a field experiment indicate that placement of N fertilizer in the center of a ridge reduces NO[subscript]3-N leaching as contrasted to a similar placement for flat tillage, even though total water movement through both systems is comparable. Vertical NO[subscript]3-N movement is predominant (in contrast to horizontal movement) and increases as the amount of simulated rainfall increases;Results from model verification indicate that the two-dimensional model has potential application in predicting water and solute movement in the unsaturated soil profile. However, further modeling activities are needed (with additional subroutines to handle runoff-ponding conditions) to insure the validity of the model for microscale applications such as those in this particular study. With further refinements, the model should be a more useful tool to describe water and chemical movement through soil for various fertilizer placements and surface configurations

    SAMFT2D: Single-phase and multiphase flow and transport in 2 dimensions. Version 2, Documentation and user`s guide

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