Finite Element Simulation of Saturated-Unsaturated Subsurface Flow

A two-dimensional transient model for flow through saturated-unsaturated porous media is developed, The model numerically solves the pressure head dependent or moisture content dependent form of Richard\u27s equation. The model code uses isoparametric quadratic triangular and/or quadrilateral finite elements for the geometric representation and for the weak Galerkin spacial integrations. An implicit, unconditionally stable single-step numerical time integration scheme with an oscilliatory noise reduction option is utilized for the temporal discretization. The highly efficient symmetric skyline (profile) solution scheme is used to solve the resulting simultaneous equations. The nonlinear subsurface flow parameters are approximated using cubic spline interpolation. The element material properties can be independently defined thus permitting the modelling of layered geologic formations, Derivative smoothing is presented for the post-calculation of Darcian velocities. Currently, the program is limited to time varying specification of pressure head or moisture content and fluxes. Several sample problems are presented illustrating the accuracy and validity of the developed model

A semi-analytical finite element method for a class of time-fractional diffusion equations

postprin

An Anlaysis of Methods for Modeling Advective-Dominated Transport

Finite element modeling of sharp front advective-dispersive-reactive transport is not accurate for highly advective or reactive problems. Two techniques were studied with the goal of accurately modeling these problems: an h-adaptive method that adjusted element lengths, and Petrov-Galerkin upwinding which used weighting functions of higher polynomial order than that of the basis functions. Finite element models were constructed using linear and quadratic basis functions in one spatial dimension. The h-adaptive method was shown to give good results with linear and quadratic basis functions. Petrov-Galerkin upwinding also yielded excellent results. This method was implemented for both classes of basis functions, but was studied only for the linear case. The benefits of Petrov-Galerkin upwinding depend on user defined parameters that regulate the amount of upwinding applied to the solution. Taylor series and Fourier analyses of the finite element truncation error as well as numerical experimentation were performed to define optimal upwinding parameters. Published results by other investigators were reproduced, and an automated method of deriving optimal upwinding parameters was developed. Analysis and operation of the Petrov-Galerkin models indicated that optimal levels of upwinding are a function of the gradient across each element. This observation led to a new upwinding scheme that adjusts the upwinding condition at each element as a function of the local gradient. Significantly better results were obtained with the new method relative to existing Petrov-Galerkin formulations. The utility of this technique will be greatly enhanced when optimal upwinding conditions are described as a function of dimensionless model parameters such as Peclet, Courant, and Damkohler numbers, and the method is generalized to multiple spatial dimensions.Master of Science in Environmental Engineerin

Finite element analysis of groundwater contamination

Includes bibliographical references.The purpose of this study was to develop a computational Finite Element model, validated by experimentation, to assist in the understanding of groundwater contamination problems. It was mainly aimed at studying the extent and manner of travel of contaminants in the saturated soil of unconfined aquifers which may be pumped by of wells

Modelling of advection-dominated transport in fluid-saturated porous media

The modelling of contaminant transport in porous media is an important topic to geosciences and geo-environmental engineering. An accurate assessment of the spatial and temporal distribution of a contaminant is an important step in the environmental decision-making process. Contaminant transport in porous media usually involves complex non-linear processes that result from the interaction of the migrating chemical species with the geological medium. The study of practical problems in contaminant transport therefore usually requires the development of computational procedures that can accurately examine the non-linear coupling processes involved. However, the computational modelling of the advection-dominated transport process is particularly sensitive to situations where the concentration profiles can exhibit high gradients and/or discontinuities. This thesis focuses on the development of an accurate computational methodology that can examine the contaminant transport problem in porous media where the advective process dominates.The development of the computational method for the advection-dominated transport problem is based on a Fourier analysis on stabilized semi-discrete Eulerian finite element methods for the advection equation. The Fourier analysis shows that under the Courant number condition of Cr=1, certain stabilized finite element scheme can give an oscillation-free and non-diffusive solution for the advection equation. Based on this observation, a time-adaptive scheme is developed for the accurate solution of the one-dimensional advection-dominated transport problem with the transient flow velocity. The time-adaptive scheme is validated with an experimental modelling of the advection-dominated transport problem involving the migration of a chemical solution in a porous column. A colour visualization-based image processing method is developed in the experimental modelling to quantitatively determinate the chemical concentration on the porous column in a non-invasive way. A mesh-refining adaptive scheme is developed for the optimal solution of the multi-dimensional advective transport problem with a time- and space-dependent flow field. Such mesh-refining adaptive procedure is quantitative in the sense that the size of the refined mesh is determined by the Courant number criterion. Finally, the thesis also presents a brief study of a numerical model that is capable to capture coupling Hydro-Mechanical-Chemical processes during the advection-dominated transport of a contaminant in a porous medium

Modeling Three-Dimensional Groundwater Flow and Solute Transport by the Finite Element Method With Parameter Estimation.

A general, systematic and improved numerical formulation for the three-dimensional (3-D) groundwater flow and solute transport problems was derived, using the finite element method. In the numerical formulation, a hidden mistake, which has appeared in many textbooks and journal papers dealing with the advective term of the general 3-D solute transport equation, was found and corrected. Some simpler and practical expressions for the leaky boundary condition, surface flux condition, and sources and sinks were proposed. To improve the conventional formulation for the time derivatives, a combination of the Galerkin method and the collocation method was developed. A more accurate scheme was derived to solve the resulting system of ordinary differential equations using the finite integration. Based on the numerical formulations, three computer models were developed for modeling (1) 3-D steady groundwater flow, (2) 3-D unsteady groundwater flow, and (3) 3-D solute transport. These models are rather general in terms of initial conditions, boundary conditions, and fluid and aquifer properties. The three models were tested using a variety of one-dimensional and two-dimensional analytical solutions and numerical models. Computed results showed that all these models are relatively simple, stable and accurate, and have little chance of experiencing any numerical problems. Component and parameter sensitivity analyses were also made. In general, these models are relatively insensitive to time step size, and the new solute transport model yields reasonable results even if the Peclet number reaches 50. In order to estimate model parameters, a fast, reliable, and derivative-free subroutine was developed by combining the quadratic interpolation search, the Golden section search, and the side-search algorithms, for finding the minimum of any user-defined 1-D function. With this 1-D subroutine, a general conjugate gradient search program was then developed to find the optimal set of parameters for any type of model. The program was tested using a variety of analytical functions and found to be accurate, fast and efficient. The program was applied to estimate parameters of the 3-D solute transport model, using two types of sampling methods and four types of data sets