Search

Simulating groundwater flows in heterogeneous aquifers is one of the most widely studied problems. The heterogeneity is modeled through random hydraulic conductivity fields log-normally distributed. In this paper, we aim to generate the realization of the log-normal hydraulic conductivity by summing up a finite number of random periodic modes with the Kraichnan algorithm. To address Neumann conditions, we propose a change of variables that results in Dirichlet boundary conditions along all boundaries of the computational domain. Then, we suggest using the radial basis function partition of unity method (RBFPUM) and RBFPUM with QR factorization (RBFPUM-QR) to analyze groundwater flow in the heterogeneous porous medium. We evaluate the performance of the proposed methods by increasing the number of random modes and the variance of the log-hydraulic conductivity fields using Gaussian and exponential correlation. In addition, we verify the effectiveness of the presented approaches in one and two dimensions using the method of manufactured solutions. Furthermore, we provide statistical inferences through Monte Carlo simulations. Numerical results demonstrate that RBFPUM-QR performs well in handling higher heterogeneity in both single realizations and Monte Carlo simulations. • A meshless numerical approach based on RBFs is proposed to solve Darcy's equation with a random hydraulic conductivity. • We use the Kraichnan algorithm to generate the log-normal hydraulic conductivity which is used to describe the heterogeneity. • The proposed approach avoids technical issues encountered in the case of an exponential correlation of the hydraulic conductivity. • The proposed numerical approach performs well to cope with higher heterogeneity. [ABSTRACT FROM AUTHOR]

In-situ bioremediation is a cost-effective technique to eliminate petroleum hydrocarbons from groundwater. In previous studies, this has been mostly applied under the approximation of a homogeneous porous medium, even though in reality aquifers are often characterized by significant heterogeneities. Here, different heterogeneous and equivalent homogeneous hydraulic conductivity fields are considered to study the effect of aquifer heterogeneity on optimal in-situ bioremediation. For this, the multiobjective simulation-optimization (S/O) model referred to as BIOEFGM-NSGA II is proposed — which uses the element-free Galerkin method (EFGM) for discretization of the governing equations, and the non-dominated sorting genetic algorithm II (NSGA II) for multiobjective optimization. This model is then applied to different heterogeneous conductivity fields generated through a pseudo-random correlated field generator for different combinations of variance and correlation lengths with constant mean. Results show that the optimal pumping policy for an equivalent homogeneous conductivity field violates the constraint of maximum allowable concentration in all the studied heterogeneous fields. To satisfy this constraint, in-situ bioremediation cost increases by 8.47% to 56.83% to that of a homogeneous field. It shows the significance of aquifer heterogeneity in designing an optimized in-situ bioremediation system and hence, should be incorporated in the S/O model for in-situ groundwater bioremediation. • BIOEFGM-NSGA II based S/O model is proposed for in-situ bioremediation. • The proposed model is applied to several random heterogeneous conductivity fields. • Optimal pumping policy of homogenous field is inefficient in heterogeneous fields. • Bioremediation cost increases on including the aquifer heterogeneity in S/O model. [ABSTRACT FROM AUTHOR]

The motivation of this present theoretical investigation comes from the delivery of various drugs and vaccines through subcutaneous injection (SCI) to the human body. In the SCI procedure, a medical person takes a big pinch of skin of the injection applicable area of a patient to pull the subcutaneous layer (SCL) from the underlying muscle layer to smooth the execution of the procedure. Generally, the human skin, particularly SCL, is a heterogeneous and anisotropic living material. The major constituents of the SCL are adipose cells or fat cells and interstitial fluid. These adipose cells are oriented in such a way that the hydraulic conductivity of the SCL exhibits anisotropy. Consequently, one can adopt the field equations of mixture theory to describe the continuum nature of SCL. This mathematical modeling involves a perturbation technique where the small aspect ratio of the SCL provides a valid perturb parameter. This study highlights the issue of the mechanical response of the adipose tissue in terms of the anisotropic hydraulic conductivity variation, the viscosity of the injected drug, the mean depth of subcutaneous tissue, etc. In particular, the computed stress fields can measure the intensity of pain experienced by a patient after this procedure. Also, this study discusses the biomechanical impact of the creation of one or more eddy structure(s) due to the high pressure developed, increased tissue anisotropy, fluid viscosity, etc., within the area of applying injection. [ABSTRACT FROM AUTHOR]