Article

Three-dimensional finite element modeling of pollutant transport in aquifers /

January 1986

Authors:

Pao-Chiang Yuan

Jackson State University

In this study, Galerkin's finite element method is used to analyze the transport of a pollutant in a three-dimensional aquifer system. The collection of water quality data is expensive, and to gather information on the migration of contaminant plumes under field conditions is a lengthy process. Therefore, a numerical model is an excellent complementary tool which can predict the future migration of a plume in saturated aquifers. The method requires that the continuous variables be replaced with discrete variable elements. Each discrete subregion is modeled with the same transport equation. The concentrations are assembled at all nodes and solved on the IBM 3081K computer. The developed model has been validated against the existing analytical and numerical solutions in one, two, and three dimensions.

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A forward particle tracking technique in an Eulerian Lagrangian numerical scheme for the solute tran...

January 2000

In this paper an eulerian-lagrangian finite element scheme developed to model the propagation of a contaminant in an unsaturated porous medium in one dimensional flow field is shown. The basic concept of this model is the different treatment of the two main transport components: the convective and the diffusive fluxes. The advective component is solved using the forward particle tracking with the ... [Show full abstract] characteristic lines method (Lagrangian procedure); the diffusive component is treated adopting the finite element method with a Galerkin scheme on a fixed grid (eulerian procedure). Efficient algorithms are applied to update the concentration of the particles in the lagrangian component of the model on the basis of the calculations carried on in the eulerian procedure and to interpolate the concentration of the pollutant particles on the nodes of the eulerian grid. As application the case of a continuous input of pollutant from the ground surface in the unsaturated porous medium is considered in comparison with a semi-analytical solution by Wilson and Gelhar (1981); the numerical solutions (with Peclet number of about 1) fit very well the analytical ones. The pollutant input in a finite time is then analyzed to investigate the influence of the Courant number of the calculations.

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Finite Element-Based Seepage Design Charts for Sheet Piles Penetrating Heterogeneous Media

January 1999 · Transportation Research Record Journal of the Transportation Research Board

Seepage and exit-gradient quantities due to flow around sheet piles embedded in geological strata are of great significance to geotechnical bridge foundation engineers because these quantities play an essential part in producing an overall economical and efficient design. In this research study, an effective and accurate method for obtaining seepage and exit-gradient estimates under similar ... [Show full abstract] hydraulic structures was developed. To achieve this objective, the finite element method was successfully implemented for providing seepage and exit-gradient estimates under single sheet piles penetrating heterogeneous media. The data obtained from the numerical model were compiled and plotted to form different sets of design charts. These charts could be used efficiently for obtaining seepage and exit-gradient estimates under the aforementioned hydraulic structure. The results obtained from the finite element model were compared and verified against existing relevant mathematical approximation and other techniques. Designers and practitioners in the geotechnical bridge engineering fields would greatly benefit from these charts because of their simple yet accurate estimates. Moreover, the applicability of the developed design charts was demonstrated through solution of various design problems.

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November 2016

This paper describes the main stages of development of a numerical tool dedicated to the modeling of the magnetoelectric effect. The proposed approaches enable to take into account the nonlinearities of the material, a static and dynamic excitation and a transient state. The developed models are based on the finite element method in 2 or 3 D. To reduce the computation time of frequency-dependent ... [Show full abstract] numerical models, the Proper Generalized Decomposition, which is a Model Order Reduction method, is introduced. Each proposed model is illustrated with an application example. The presented work is based on the contributions of three French laboratories: GeePs, L2E and L2EP.

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Numerical modeling and analysis of the damage characteristics of a honeycomb core within a sandwich...

Brandon M Wilkins

Sandwich panels increasingly replace metallic components in the aerospace industry. The sandwich panel configuration that is being considered in this research project is composed of carbon fiber composite facesheets encasing a honeycomb core. The honeycomb core is made from a fibrous sheet of material constructed into hexagonal cells. The core is relatively compliant compared to the composite ... [Show full abstract] facesheet, but together in a sandwich panel they result in a structure that has both desirable strength to weight and stiffness to weight ratios. As these composite structures are integrated into the design of aircraft, an understanding of their failure modes and an accurate prediction of their structural integrity when damaged are essential. The objective of this research is to understand how individual failure mechanisms contribute to the mechanical response of the overall material system. Damage mechanisms associated with sandwich panels include failure of the composite facesheets, crushing of the honeycomb core and disbonding at the interface between the composite and the core. To understand how such damage affects the response of the material system, a finite element model incorporating the dominant failure modes was created. Simulations of the sandwich structure needed to be computationally efficient and accurately demonstrate the failure characteristics that were observed experimentally. Experimental results showed that damage in the honeycomb could initiate without any visible damage to the facesheet, so the analysis of the honeycomb was especially important to the integrity of the model. In order to account for the damage in the honeycomb, a novel crushing zone model was developed to capture the failure response of the core. Facesheets were modeled using a plane stress orthotropic material formulation, and the Hashin-Rotem (1973) damage criterion was used to account for the initiation and propagation of the failure within the composite. The finite element model (FEM) was created and analyzed with the ABAQUS/Standard software package. FEM results show that failure of the core is present in shallow indentations and low energy impacts. Core failure will initiate prior to the failure of the composite and will always present a larger damaged area, which illustrates the importance of analyzing the material.

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Finite element wave model for Laplace equation

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The mild-slope equation has been used for calculation of the surface gravity water wave transformation. Recently, its extended versions were introduced, which is capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. Here, we develop a new finite element model to solve the Laplace equation directly while ... [Show full abstract] keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of the wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to get a finite element solution. The computational domain is discretized with an infinite element. The applicability of the developed model is verified through example analyses of two-dimensional wave reflection and transmission.

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Static and Dynamic Analysis of Thick Functionally Graded Plates with Piezoelectric Layers Using Laye...

November 2009 · Mechanics of Advanced Materials and Structures

In this paper, static and dynamic analysis of a functionally graded material (FGM) plate with surface-bonded piezoelectric layers is studied. A general finite element formulation based on the layerwise theory is developed for modelling an FG plate with piezoelectric layers or patches. The intermediate FG layer is assumed to be made of many sublayers. Each sublayer is considered as an isotropic ... [Show full abstract] layer with constant material properties calculated by the rule of mixtures at the bottom of sublayer. The developed FE model is used for analyzing the quasi-static, free vibration and response of plate to impulse loads. The effects of span-to-thickness ratio and the volume fractions of constituents on the natural frequencies, transverse and in-plane deflections, stress distribution and induced electric potential in piezoelectric layers are scrutinized and the results are compared with the previously reported analytical and numerical works in the literature, where available. It is shown that by using the proposed three-dimensional based finite element model, static and dynamic analysis of thin to thick FG plates with bonded piezoelectric layers can be performed with sufficient accuracy. Also, the non-linear distribution of electric potential in thick piezoelectric layers, which is ignored by most previous works, can be captured using the proposed model.

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June 1989 · Advances in Water Resources

The numerical models represent very useful tools for the simulation of regional flows and may provide several indications as to a rational management and allocation of the available water resources. The very complex aquifer systems underlying the Friuli-Venezia Giulia Region in northeastern Italy, has been analysed with the aid of two combined models based on the finite element method. The first ... [Show full abstract] model simulates the steady flow in the Upper Plain and relies on the Dupit-Forchheimer—Boussinesq approach. The second one simulates the multi-aquifer basin of the Lower Plain and is based on the integro-differential theory of flow. Both models have been run under a series of realistic assumptions properly combined with the limited available information. The results obtained for the dry regime are moderately satisfactory and allow for the first-hand appraisal of the quantity involved in the overall regional groundwater balance. They also point out the need for a substantial improvement in the quality and quantity of the regional subsurface data vis à vis reliable future predictions in a wider framework of practical interest.

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A study of convective-dispersion equation by isoparametric finite elements

January 1975 · Journal of Hydrology

The transport of pollutants in ground-water aquifers is studied by means of a mathematical model and presented here. The governing equation for the movement of impurities takes the form of a convective-dispersion equation which is solved numerically using isoparametric, quadrilateral finite element method. The mixed boundary conditions and irregular distribution of the nodes can be handled easily ... [Show full abstract] by the finite element technique. The calculations show that the numerical model could be used as an effective means to predict the distribution of contaminant and to shed light on the ground-water pollution control.

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A simple explicit, characteristic-based finite element method for the numerical simulation of the dispersion of the thermal outflow in Huelva estuary is considered in this paper. The derivation involves a local Taylor expansion of the convection–diffusion equation. The numerical model used was originally designed to simulate the dispersion of pollutants in the open sea and has now been ... [Show full abstract] reconfigured to simulate the dispersion of the thermal outflow of some power plants which may be constructed in Huelva estuary in the near future. Numerical results obtained are presented.

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Effect of Carbon Black on Temperature Field and Weld Profile During Laser Transmission Welding of Po...

April 2012 · Optics & Laser Technology

The influence of the carbon black on temperature distribution and weld profile, during laser transmission welding of polymers, is investigated in the present research work. A transient numerical model, based on conduction mode heat transfer, is developed to analyze the process. The heat input to the model is considered to be the volumetric Gaussian heat source. The computation of temperature ... [Show full abstract] field during welding is carried out for polycarbonates having different proportion of carbon black in polymer matrix. The temperature dependent material properties of polycarbonate are taken into account for modeling. The finite element code ANSYS® is employed to obtain the numerical results. The numerically computed results of weld pool dimensions are compared with the experimental results. The comparison shows a fair agreement between them, which gives confidence to use the developed model for intended investigation with acceptable accuracy. The results obtained have revealed that the carbon black has considerable influence on the temperature field distribution and the formation of the weld pool geometry.

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The present study investigated the application of finite element method for prediction of mechanical properties of quench hardening steel. Based on the experimental results obtained, a numerical model for simulation of continuous cooling of quench hardening steel was developed. For the simulation of the kinetics of diffusion phase transformations, the Avrami equation and additive rule were ... [Show full abstract] applied. A new model was also developed for martensitic transformation which was validated using metallographic analysis and hardness tests. Experimental and simulation results indicated a good agreement. The developed model information provided here could be used for simulation of continuous cooling and kinetics phase transformation as well as for prediction of final distribution of microstructures and hardness of alloy steels.

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Numerical Modeling of Heterogeneous Moisture Diffusion in Milled Rice Grains: Diffusion Coefficient...

January 2014 · Food Science and Technology Research

The heterogeneous moisture diffusion of milled rice grains at 25, 35 and 45 °C was simulated in 3D using the finite element method. The objectives of the study were to investigate the effects of temperature on moisture absorption and to predict the heterogeneous moisture diffusion in milled rice grains. Major routes and cracks channeled and facilitated rapid moisture movement in the grain. High ... [Show full abstract] temperature increased the rate of moisture movement. The moisture diffusion coefficient expressed as a function of moisture, temperature and time adequately described the heterogeneous moisture diffusion characteristics in milled rice. The integration of the logistic function of time reduced the root mean square error (RMSE) values between the experimental data and the numerical solution. Moreover, the RMSE values were much lower than the values modeled with moisture and temperature only. Modeling moisture transfer using the major routes of moisture revealed an increase in the modified frequency factor of the moisture diffusion coefficient.

Last Updated: 05 Jul 2022