In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).
A 2D hydrodynamic (labeled as CAR) model has been proposed in a rectangular Cartesian coordinate system with two axes within the horizontal plane and one axis along the vertical direction (global coordinates), considering the effects of bed slope on both pressure distribution and bed shear stresses. The CAR model satisfactorily reproduces the analytical solutions of dam-break flow over a steep slope, while the traditional Saint-Venant Equations (labeled as SVE) significantly overestimate the flow velocity. For flood events with long duration and large mean slope, the CAR and the SVE models present distinguishable discrepancies. Therefore, the proposed CAR model is recommended for applications to real floods for its facility of extending from 1D to 2D version and ability to model shallow-water flows on steep slopes.
Mathematical modelling is shown as an efficient tool for studying the behaviour of reservoir ecosystems. Two mathematical models, namely ASTER and DYRESM-WQ and their characteristic features are described. The parameters of both models and their values used for simulation of reservoir Rimov are presented. Sensitivity analysis for both models was performed in the scope to demonstrate the sensitivity of simulation results to the parameter changes. The simulation results were compared to the measurements in situ with satisfying accuracy. The suitability of application of both models on the food web simulation of valley reservoirs is discussed. and Článek ukazuje matematické modelování jako účinný prostředek pro studium chování ekosystémů údolních nádrží. Popisuje dva matematické modely, a to ASTER a DYRESM-WQ, a jejich charakteristické rysy. Podrobně jsou ukázány parametry obou modelů a rovněž jejich hodnoty, jichž bylo použito k simulaci údolní nádrže Římov. Pomocí citlivostní analýzy byla zjištěna u obou modelů velikost odezvy systému na změny některých parametrů. Porovnání výsledků simulací s hodnotami naměřenými v nádrži ukazuje dostatečnou přesnost matematického modelování. V závěru je diskutována vhodnost použití matematického modelování pro simulaci potravního řetězce v údolních nádržích.