Department of Civil Engineering

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Browsing Department of Civil Engineering by Subject "Advection"

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    Modelling breakthrough curves and investigating the impact of models and numerical properties on parameter estimation
    (Stellenbosch : Stellenbosch University, 2019-04) Silavwe, Davy Danny; Brink, I. C.; Stellenbosch University. Faculty of Engineering. Dept. of Civil Engineering.
    ENGLISH ABSTRACT: The research investigated and applied several Eulerian numerical methods of the advection-dispersion model (AD-Model) for the analysis of concentration-time curves, also known as breakthrough curves (BTCs), to develop empirical models for predicting stream longitudinal dispersion coefficients. Typically, measured BTCs are analysed to estimate solute transport parameters which are then used to develop empirical equations by correlating optimised longitudinal dispersion coefficients with the bulk flow and channel properties. The investigation attempted to determine the impact of numerical methods and nondimensional numerical properties on optimised parameters and subsequently on constructed empirical models for predicting longitudinal dispersion coefficients. Four concerns related to the construction of empirical models for estimating stream longitudinal dispersion coefficient based on estimates by numerical methods were addressed. (a) Dependence of estimated parameter values on the method used. (b) Influence of numerical properties on values of estimated parameters (c) Identification of model structure, and (d) Characterising model performance. To address the concern (a), six optional numerical methods were assessed using a set of synthetic BTCs simulated for a hypothetical stream reach. This was followed by a selection of three numerical methods for the analysis of observed BTCs to determine parameter values for the development of empirical models. The selected numerical methods are well-known methods, namely, Backward-time/centred space (BTCS), Crank-Nicolson, Implicit QUICK, QUICKEST, MacCormack and third-order upstream-differencing methods. Shortlisted methods were Crank-Nicolson, MacCormack and QUICKEST methods. To address issue (b) parameter values for the development of empirical models were obtained over a range of numerical properties. To address issue (c) dimensional analysis and least-squares regression was used. To address issue (d) a combination of several model performance measures focusing on several features were used for a broad evaluation of models. The study shows that optimal parameter values of the AD-Model determined by Eulerian numerical methods vary with numerical methods and model resolution, such that there is a possibility of overestimating or underestimating parameter values, especially the dispersion coefficient. Consequently, in this research, the Crank-Nicolson and the MacCormack methods were observed to overpredict the dispersion coefficient with an increase in Peclet number, while the the QUICKEST method was observed to underpredict dispersion coefficients with increase in Peclet number. Consequently, structures of developed empirical models and predictions varied with solution method used and nondimensional numerical parameters under which optimised parameters were determined. Based on performance analysis measures, adequate and comparable empirical models were developed for a range of 0.599 – 12.818 of the Peclet number. However, the quality of concentration predictions using predicted dispersion coefficients requires the use of numerical methods and model resolutions under which empirical models were developed. Therefore, empirical models may be well-founded within their calibrated conditions and channel characteristics.