Epaminondas Sidiropoulos

Similarity and iterative solution of the Boussinesq equation

Abstract The one-dimensional Boussinesq equation is used to describe groundwater flow from a stream to an aquifer due to sudden raising of the stream level. Applications are also noted in diffusion and heat conduction problems with a step-function increase in their boundary values. Through the Boltzmann transformation an ordinary nonlinear differential equation and a two-point boundary value problem is obtained, which is solved by means of shooting iterations. Qualitative considerations permit the construction, through fitting, of an analytical curve that provides an estimate of the slope at the origin, needed for the first shooting iteration. A new formula is proposed for the slope needed in the second iteration. Finally, an algorithm is given that produces first- and second-order corrections to the previous slope estimates until the solution given by the Runge-Kutta scheme yields the desired value at infinity. The latter estimates combined with the iterative scheme remove the necessity of large numbers of shooting iterations.

Machine Learning Utilization for Bed Load Transport in Gravel-Bed Rivers

Three data-driven techniques, namely artificial neural networks, adaptive-network-based fuzzy inference system, and symbolic regression based on genetic programming, are employed for the prediction of bed load transport rates in gravel-bed steep mountainous streams and rivers in Idaho (U.S.A.), and the potential of several input variables is investigated. The input combinations that were tested are based, mainly, on unit stream power, stream power, and shear stress, and exhibited similarly good performance, with respect to the machine learning technique used, accentuating the importance of the regression model. The derived models are robust, generalize very well in unseen data, and generated results superior to those of some of the widely used bed load formulae, without the need to set a threshold for the initiation of motion, and consequently avoid predicting erroneous zero transport rates.

Sensitivity analysis of closed-form analytical hydraulic conductivity models

The three parameters α, n and m in the Van Genuchten analytical soil-moisture characteristic curve are considered to be independent in this paper. The three-parameter fitting problem that arises is reduced to a one-dimensional minimization search, through a suitable transformation. The resulting unidimensional algorithm is amenable to analysis. Its qualitative characteristics are derived and the existence of a minimum is established. The values of the parameters thus obtained are introduced as starting estimates in a three-parameter minimization process of the Newton-Raphson type. As a continuation of this, a sensitivity analysis is formulated of the unsaturated hydraulic conductivity with respect to the residual (θr) and the saturated (θs) water content. The entire analysis is applied to the retention data of five selected soils of different hydraulic properties. In all cases considered, the very good fit offered by the unidimensional algorithm is demonstrated. Also, the sensitivity of the hydraulic conductivity shows a drastic increase in the range of lower water contents, and the sensitivity with respect to θs maintains nonnegligible values over the whole water content range.

Assessment of sediment transport approaches for sand-bed rivers by means of machine learning

Abstract The quantification of the sediment carrying capacity of a river is a difficult task that has received much attention. For sand-bed rivers especially, several sediment transport functions have appeared in the literature based on various concepts and approaches; however, since they present a significant discrepancy in their results, none of them has become universally accepted. This paper employs three machine learning techniques, namely artificial neural networks, symbolic regression based on genetic programming and an adaptive-network-based fuzzy inference system, for the derivation of sediment transport formulae for sand-bed rivers from field and laboratory flume data. For the determination of the input parameters, some of the most prominent fundamental approaches that govern the phenomenon, such as shear stress, stream power and unit stream power, are utilized and a comparison of their efficacy is provided. The results obtained from the machine learning techniques are superior to those of the commonly-used sediment transport formulae and it is shown that each of the input combinations tested has its own merit, as they produce similarly good results with respect to the data-driven technique employed. Editor Z.W. Kundzewicz

Nonlinear diffusion with linearly varying diffusivity

Abstract An approximate analytical solution to the nonlinear diffusion equation is presented. The diffusivity is assumed to be linearly dependent on concentration. The one-dimensional problem is reduced to an ordinary differential equation through the Boltzmann transformation and a technique which is exploiting basic characteristics of the exact solution is developed. The technique presented here can be applied to problems of groundwater contamination, to problems of water absorption into unsaturated soils, as well as to various other engineering problems leading to the diffusion equation. A comparison of the numerical results with other methods concludes the paper.

Simplified determination and sensitivity analysis of soil-moisture retention curves and hydraulic conductivity

Abstract A simple algorithm is presented that estimates the parameters contained in the Van Genuchten analytical soil-moisture characteristic curves. No graphical estimations are involved and convergence is rapid. The values obtained from the simple algorithm are introduced as starting values in a Newton-Raphson minimization procedure which yields more accurate evaluations of the parameters. The very good approximation offered by the simple algorithm is responsible for the small number of subsequent Newton-Raphson iterations. Based on the final results of the minimization scheme an analytical sensitivity analysis is carried out with respect to changes induced in the basic parameter “residual water content”. Soils with a wide range of hydraulic properties were subjected to the above analysis. It is demonstrated that for lower water contents the sensitivity of the hydraulic conductivity becomes by 2–5 orders of magnitude larger than it is for higher ones.

Sensitivity analysis of a coupled heat and mass transfer model in unsaturated porous media

Abstract Heat and moisture transfer equations are solved and a sensitivity analysis is presented. Physical models based on equilibrium thermodynamics and models based on irreversible thermodynamics are reviewed. The governing equations are reduced to a non-dimensional form. Finite-difference and finite-element solutions are given; they are compared with analytical ones, obtained after linearization of these equations through Fourier and Laplace transforms. Moisture profiles for the linearized case are produced both for isothermal and non-isothermal conditions, demonstrating an excellent agreement between the different numerical and analytical methods. The non-isothermal profiles are seen to advance more rapidly. The small influence of the phase conversion coefficient is observed in numerical experiments. An analytical treatment of sensitivity with respect to this coefficient is presented. Sensitivity is further demonstrated by means of a numerical example. Establishment of the small effect of the above coefficient leads to significant reductions.

A Machine Learning Approach for the Mean Flow Velocity Prediction in Alluvial Channels

In natural alluvial channels, the determination of the flow resistance constitutes a problem with additional complexity compared to rigid bed channels, due to the bed morphology transformations and the alterations of the flow properties caused by sediment transport. While there have been steps towards understanding the processes that contribute to flow resistance in an alluvial channel, a robust quantitative model with wide applicability remains elusive. Machine learning offers the ability to exploit available data and generate equations that accurately describe the problem by taking implicitly into account the contributing mechanisms that are difficult to be modeled. In this paper, four machine learning techniques are employed for the mean flow velocity prediction, separately for sand-bed and gravel-bed rivers, namely artificial neural networks, adaptive-network-based fuzzy inference system, symbolic regression based on genetic programming, and support vector regression. The derived models are robust and their results are superior to those of some widely used flow resistance formulae, which compute the mean flow velocity from similar independent hydraulic variables.

Derivation of Sediment Transport Models for Sand Bed Rivers from Data-Driven Techniques

Hydraulic engineers and geologists have studied sediment transport in natural streams and rivers for centuries due to its importance in understanding river hydraulics. Erosion and deposition of sediment alters the hydraulic geometry of the channel and may cause increase of flood frequency as well as navigation problems from excessive deposition. Moreover, dis‐ charge of industrial and agricultural residuals sets the sediment particles to be the primary transporters of toxic substances that contaminate aquatic systems. High sediment discharge peaks may be destructive for fish habitats and ecosystems, and long-term sediment yield af‐ fects the design and function of constructions such as dams and reservoirs, as well as the coastal erosion at the basin outlet.

Modelling of discontinuities through dipole distribution

Abstract An indirect boundary element method using dipole distribution is employed in order to model discontinuities inside the flow region. The problem of flow under a dam is treated with a sheet-pile in its foundation. The discontinuity across the sheet-pile is demonstrated, a general boundary element procedure for a mixed problem is outlined and the coefficients of the linear system are given in analytical form. Very good agreement with existing analytical results is obtained.