The paper discusses problem of deep conduit evolution in karst aquifers. Uncritically accepted hypothesis of Worthington claims that deep flow pathways are prone to speleogenesis as the viscosity diminishes with increase of temperature when the water penetrates into deep structures. Our model opposes the claim and clearly demonstrates that other mechanisms, which make deep speleogenesis less favourable prevail. Among them decrease of initial openings due to the lithostratigraphic stress and decrease of solubility with depth are the most important.

COBISS.SI-ID: 37575981

In this paper, a solution of a two-dimensional (2D) Stokes flow problem, subject to Dirichlet and fluid traction boundary conditions, is developed based on the Non-singular Method of Fundamental Solutions (NMFS). The Stokes equation is decomposed into three coupled Laplace equations for modified components of velocity, and pressure. The solution is based on the collocation of boundary conditions at the physical boundary by the fundamental solution of Laplace equation. The singularities are removed by smoothing over on disks around them. The derivatives on the boundary in the singular points are calculated through simple reference solutions. In NMFS no artificial boundary is needed as in the classical Method of Fundamental Solutions (MFS). Numerical examples include driven cavity flow on a square, analytically solvable solution on a circle and channel flow on a rectangle. The accuracy of the results is assessed by comparison with the MFS solution and analytical solutions. The main advantage of the approach is its simple, boundary only meshless character of the computations, and possibility of straightforward extension of the approach to three-dimensional (3D) problems, moving boundary problems and inverse problems.

COBISS.SI-ID: 3547899

The purpose of the present paper is to develop a Non-singular Method of Fundamental Solutions (NMFS) for two-dimensional anisotropic linear elasticity problems.The NMFS is based on the classical Method of Fundamental Solutions (MFS) with regularization of the singularities. This is achieved by replacing the concentrated point sources with distributed sources over disks around the singularity, as recently developed for isotropic elasticity problem. In case of the displacement boundary conditions, the values of distributed sources are calculated by a simple numerical procedure, since the closed form solution is not available. In case of traction boundary conditions, the respective desingularized values of the derivatives of the fundamental solution in the coordinate directions, as required in the calculations, are calculated indirectly by considering two reference solutions of the linearly varying simple displacement fields. The feasibility and accuracy of the newly developed method are demonstrated through comparison with MFS solutions and analytical solutions for a spectra of anisotropic plane strain elasticity problems, including bi-material arrangements. NMFS turns out to give similar results as the MFS in all spectra of performed tests. The lack of artificial boundary is particularly advantageous for using NMFS in multi-body problems, where MFS completely fails.

COBISS.SI-ID: 3222779

A novel numerical model is presented, that simulates evolution of karst conduit network in transition from pressurised to free surface flow. Several new mechanisms of flow pathway selection in karst aquifers are described.

COBISS.SI-ID: 37810733