Groundwater Processes and Modelling - Part 6

1998 ◽  
Author(s):  
D Armstrong ◽  
K Narayan
Keyword(s):  
Steady State ◽  
Groundwater Flow ◽  
Model Calibration ◽  
Numerical Models ◽  
Inverse Modelling ◽  
Governing Equations ◽  
Geological Materials ◽  
Recent Developments ◽  
Modelling Techniques ◽  
Calibration Tool

This booklet outlines the properties of geological materials which enable them to accept, store and transmit groundwater, together with a description of the principal types of aquifer which are commonly found to occur in the field. Sources of groundwater are described in order to provide an understanding of the hydrogeological modelling exercise. The governing equations for steady state and non-steady state (transient) groundwater flow, are presented together with a brief overview of a range of modelling techniques, including both analytical and numerical models, the use of diffuse recharge as a model calibration tool and recent developments in the field of inverse modelling are also discussed.

scholarly journals Application of Meshless local Petrov-Galerkin approach for steady state groundwater flow modeling

2022 ◽  
Author(s):  
Ali Mohtashami ◽  
Seyed Arman Hashemi Monfared ◽  
Gholamreza Azizyan ◽  
Abolfazl Akbarpour
Keyword(s):  
Steady State ◽  
Numerical Methods ◽  
Groundwater Flow ◽  
Unconfined Aquifer ◽  
Real Field ◽  
Flow Modeling ◽  
Governing Equations ◽  
The Third ◽  
Mlpg Method ◽  
Good Agreement

Abstract The complicated behavior of groundwater system in an arid aquifer is generally studied by solving the governing equations using either analytical or numerical methods. In this regard, analytical methods are just for some aquifers with regular boundaries. Numerical methods used for this aim are finite difference (FDM) and finite element methods (FEM) which are engaged for some simple aquifers. Using them in the complex cases with irregular boundaries has some shortcomings, depended on meshes. In this study, meshless local Petrov-Galerkin (MLPG) method based on the moving kriging (MK) approximation function is used to simulate groundwater flow in steady state over three aquifers, two standard and a real field aquifer. Moving kriging function known as new function which reduces the uncertain parameter. For the first aquifer, a simple rectangular aquifer, MLPG-MK indicates good agreement with analytical solutions. In the second one, aquifer conditions get more complicated. However, MLPG-MK reveals results more accurate than FDM. RMSE for MLPG-MK and FDM is 0.066 and 0.322 m respectively. In the third aquifer, Birjand unconfined aquifer located in Iran is investigated. In this aquifer, there are 190 extraction wells. The geometry of the aquifer is irregular as well. With this challenging issues, MLPG-MK again shows satisfactory accuracy. As the RMSE for MLPG-MK and FDM are 0.483 m and 0.566 m. therefore, planning for this aquifer based on the MLPG-MK is closer to reality.

scholarly journals Recent Developments in the Modelling of Transformer Windings

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2798
Author(s):  
Konstanty M. Gawrylczyk ◽  
Szymon Banaszak
Keyword(s):  
Literature Review ◽  
Research And Development ◽  
Frequency Response ◽  
Input Data ◽  
Recent Developments ◽  
Modelling Techniques ◽  
Lumped Parameters ◽  
Wave Phenomena ◽  
Modelling Methods ◽  
Direct Calculations

The paper provides a review of the modelling techniques used to simulate the frequency response of transformer windings. The aim of the research and development of modelling methods was to analyze the influence of deformations and faults in the windings on the changes in the frequency response. All described methods are given with examples of the modelling results performed by the authors of this paper and from literature sources. The research is prefaced with a thorough literature review. There are described models based on lumped parameters with input data coming from direct calculations based on the winding geometry and obtained from FEM modelling software and models considering the wave phenomena in the windings. The analysis was also performed for practical problems in winding modelling: the influence of windings other than the modelled one and the influence of parallel wires in a winding.

scholarly journals The Influence of Different Types of Nanofluid on Thermal and Fluid Flow Performance of Liquid Cold Plate

2018 ◽  
Vol 7 (4.35) ◽  
pp. 148 ◽  
Author(s):  
Nur Irmawati Om ◽  
Rozli Zulkifli ◽  
P. Gunnasegaran
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Steady State ◽  
Pressure Drop ◽  
Volume Fraction ◽  
Cold Plate ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Different Types ◽  
Volume Method

The influence of utilizing different nanofluids types on the liquid cold plate (LCP) is numerically investigated. The thermal and fluid flow performance of LCP is examined by using pure ethylene glycol (EG), Al2O3-EG and CuO-EG. The volume fraction of the nanoparticle for both nanofluid is 2%. The finite volume method (FVM) has been used to solved 3-D steady state, laminar flow and heat transfer governing equations. The presented results indicate that Al2O3-EG able to provide the lowest surface temperature of the heater block followed by CuO-EG and EG, respectively. It is also found that the pressure drop and friction factor are higher for Al2O3-EG and CuO-EG compared to the pure EG.

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

Predicting Groundwater Flow and Solute Transport in the Heterogeneous Aquifer Sandbox Using Different Parameter Estimation Methods

2021 ◽  
Author(s):  
Liqun Jiang ◽  
Ronglin Sun ◽  
Xing Liang
Keyword(s):  
Steady State ◽  
Groundwater Flow ◽  
Solute Transport ◽  
Transport Process ◽  
Homogeneous Model ◽  
Estimation Methods ◽  
Aquifer Heterogeneity ◽  
Heterogeneous Aquifer ◽  
Tracer Distribution ◽  
Parameter Estimation Methods

<p>Protection and management of groundwater resources demand high-resolution distributions of hydraulic parameters (e.g., hydraulic conductivity (K) and specific storage (Ss)) of aquifers. In the past, these parameters were obtained by traditional analytical solutions (e.g., Theis (1935) or Cooper and Jacob (1946)). However, traditional methods assume the aquifer to be homogeneous and yield the equivalent parameter, which are averages over a large volume and are insufficient for predicting groundwater flow and solute transport process (Butler & Liu, 1993). For obtaining the aquifer heterogeneity, some scholars have used kriging (e.g., Illman et al., 2010) and hydraulic tomography (HT) (e.g., Yeh & Liu, 2000; Zhu & Yeh, 2005) to describe the K distribution.</p><p>In this study, the laboratory heterogeneous aquifer sandbox is used to investigate the effect of different hydraulic parameter estimation methods on predicting groundwater flow and solute transport process. Conventional equivalent homogeneous model, kriging and HT are used to characterize the heterogeneity of sandbox aquifer. A number of the steady-state head data are collected from a series of single-hole pumping tests in the lab sandbox, and are then used to estimate the K fields of the sandbox aquifer by the steady-state inverse modeling in HT survey which was conducted using the SimSLE algorithm (Simultaneous SLE, Xiang et al., 2009), a built-in function of the software package of VSAFT2. The 40 K core samples from the sandbox aquifer are collected by the Darcy experiments, and are then used to obtain K fields through kriging which was conducted using the software package of Surfer 13. The role of prior information on improving HT survey is then discussed. The K estimates by different methods are used to predict the process of steady-state groundwater flow and solute transport, and evaluate the merits and demerits of different methods, investigate the effect of aquifer heterogeneity on groundwater flow and solute transport.</p><p>According to lab sandbox experiments results, we concluded that compared with kriging, HT can get higher precision to characterize the aquifer heterogeneity and predict the process of groundwater flow and solute transport. The 40 K fields from the K core samples are used as priori information of HT survey can promote the accuracy of K estimates. The conventional equivalent homogeneous model cannot accurately predict the process of groundwater flow and solute transport in heterogeneous aquifer. The enhancement of aquifer heterogeneity will lead to the enhancement of the spatial variability of tracer distribution and migration path, and the dominant channel directly determines the migration path and tracer distribution.</p>

Closed-form expressions for the steady-state response of damped transmission line conductors considering their bending stiffness

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1319-1329
Author(s):  
Marcelo A Ceballos ◽  
José E Stuardi
Keyword(s):  
Steady State ◽  
Transmission Line ◽  
Numerical Models ◽  
Mechanical Impedance ◽  
Steady State Solution ◽  
Bending Stiffness ◽  
Analytical Models ◽  
Dispersive Media ◽  
Overhead Transmission Line ◽  
Damper Design

This paper begins with a brief compilation of analytical models typically used to calculate the dynamic response of a conductor span belonging to an overhead transmission line, with a Stockbridge-type damper located near one of its ends. In most of analyses found in the literature, the calculation of the response is done through the superposition of waves that propagate in both longitudinal directions impinging and reflecting at the span ends and at the damper attachment points. The approach proposed in this paper allows obtaining the response as the steady-state solution of the governing differential equations providing suitable analytical expressions for conductors with bending stiffness, which are dispersive media for propagating waves. Using these analytical solutions, the influence of bending stiffness on the efficiency and on the optimal mechanical impedance of the damper, which are of great importance in damper design, can be described explicitly. At the same time, the proposed methodology avoids the need of numerical models or approximate formulas to calculate the bending strains in critical points of the conductor with a single damper.

scholarly journals Quasi-Steady State Cosmology

1994 ◽  
Vol 159 ◽  
pp. 293-299
Author(s):  
G. Burbidge ◽  
F. Hoyle ◽  
J.V. Narlikar
Keyword(s):  
Steady State ◽  
Early Universe ◽  
Particle Physics ◽  
Physical Theory ◽  
Big Bang ◽  
Quasi Steady State ◽  
Recent Developments ◽  
History Of ◽  
The Big Bang ◽  
The Universe

The standard big bang cosmology has the universe created out of a primeval explosion that not only created matter and radiation but also spacetime itself. The big bang event itself cannot be discussed within the framework of a physical theory but the events following it are in principle considered within the scope of science. The recent developments on the frontier between particle physics and cosmology highlight the attempts to chart the history of the very early universe.

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