Numerical speleogenetic models can be applied to study the tranport properties of karst aquifers at different stage of evolution. We have applied particle tracking method in such aquifers and described several mechanism leading to specific shapes of tracer breakthrough curves in karst aquifers.
COBISS.SI-ID: 33338669
Collapse dolines are among the most striking surface features in karst areas. Although they can be the result of different formation mechanisms, evidence suggests that large collapse dolines form due to chemical and mechanical removal of material at and below the level of groundwater. We have applied a genetic model of a two-dimensional fracture network to calculate the rate of dissolutional bedrock removal in the heavily fractured (crushed) zone intersecting a karst conduit in the phreatic zone. To account for infilling and breakdown processes in the crushed zone two simple rules were added to the basic model: 1) continuous infilling of dissolutionally created voids prevents fractures from growing beyond some limited aperture, although the dissolution proceeds, 2) discontinuous collapsing causes sudden closure of a fracture once some critical aperture has been reached. Both rules limit the transmissivity of the network and the related flow rates. Therefore, the constant head difference between the input and the output points is sustained and the flow remains distributed over the entire crushed zone. Provided that restrictions posed by the two rules permit turbulent flow, dissolution rates also remain high in the entire region. High surface area of water-rock contact and high dissolution rates result in high overall removal rates of rock from the crushed zone, one of the necessary conditions for the formation of large closed depressions. Despite the fact that the model neglects some processes and dynamics that would increase the removal rate, the results suggest that large closed depressions could form in the order of 1 million years.
COBISS.SI-ID: 46343010
Based on Haar wavelets an efficient numerical method is proposed for the numerical solution of system of coupled Ordinary Differential Equations (ODEs) related to the natural convection boundary layer fluid flow problems with high Prandtl number (Pr). The numerical study of these flow models is necessary as the existing literature is more focused on the flow problems with small values of Pr. In this work, the problem of natural convection which consists of coupled nonlinear ODEs is solved simultaneously. The ODEs are obtained from the Navier Stokes equations through the similarity transformations. The effects of variation of Pr on heat transfer are investigated. Performance of the Haar Wavelets Collocation Method (HWCM) is compared with the finite difference method (FDM), Runge–Kutta Method (RKM), homotopy analysis method (HAM) and exact solution for the last problem. More accurate solutions are obtained by wavelets decomposition in the form of a multi-resolution analysis of the function which represents solution of the given problems. Through this analysis the solution is found on the coarse grid points and then refined towards higher accuracy by increasing the level of the Haar wavelets. Neumann’s boundary conditions which are problematic for most of the numerical methods are automatically coped with. A distinctive feature of the proposed method is its simple applicability for a variety of boundary conditions. Efficiency analysis of HWCM versus RKM is performed using Timing command in Mathematica software. A brief convergence analysis of the proposed method is given. Numerical tests are performed to test the applicability, efficiency and accuracy of the method.
COBISS.SI-ID: 1740027