The Radius of Influence Myth

Empirical formulas to estimate the radius of influence, such as the Sichardt formula, occasionally appear in studies assessing the environmental impact of groundwater extractions. As they are inconsistent with fundamental hydrogeological principles, the term “radius of influence myth” is used by analogy with the water budget myth. Alternative formulations based on the well-known de Glee and Theis equations are presented, and the contested formula that estimates the radius of influence by balancing pumping and infiltration rate is derived from an asymptotic solution of an analytical model developed by Ernst in 1971. The transient state solution of this model is developed applying the Laplace transform, and it is verified against the finite-difference solution. Examining drawdown and total storage change reveals the relations between the presented one-dimensional radial flow solutions. The assumptions underlying these solutions are discussed in detail to show their limitations and to refute misunderstandings about their applicability. The discussed analytical models and the formulas derived from it to estimate the radius of influence cannot be regarded as substitutes for advanced modeling, although they offer valuable insights on relevant parameter combinations.

Optimal location of pumping wells by a mesh-free numerical method

In the present study, the optimal place to excavate extraction wells as the drawdown gets minimized was investigated in a real aquifer. Meshless local Petrov-Galerkin (MLPG) method is used as the simulation method. The closeness of its results to the observational data compared to the finite difference solution showed the higher accuracy of this method as the RMSE for MLPG is 0.757 m while this value for finite difference equaled to 1.197 m. Particle warm algorithm is used as the optimization model. The objective function defined as the summation of the absolute values of difference between the groundwater level before abstraction and the groundwater level after abstraction from wells. In Birjand aquifer which is investigated in transient state, the value of objective function before applying the optimization model was 2.808 m, while in the optimal condition, reached to 1.329 m (47% reduction in drawdown). This fact was investigated and observed in three piezometers. In the first piezometer, the drawdown before and after model enforcement was 0.007 m and 0.003 m, respectively. This reduction occurred in other piezometers as well.

Finite Difference Solution to a Nonlinear Time-Fractional Logistic Model

We set forth a time-fractional logistic model and give an implicit finite difference scheme for solving of the model. The L^2 stability and convergence of the scheme are proved with the aids of discrete Gronwall inequality, and numerical examples are presented to support the theoretical analysis.

A Moving-Mesh Finite-Difference Method for Segregated Two-Phase Competition-Diffusion

A moving-mesh finite-difference solution of a Lotka-Volterra competition-diffusion model of theoretical ecology is described in which the competition is sufficiently strong to spatially segregate the two populations, leading to a two-phase problem with a coupling condition at the moving interface. A moving mesh approach preserves the identities of the two species in space and time, so that the parameters always refer to the correct population. The model is implemented numerically with a variety of parameter combinations, illustrating how the populations may evolve in time.

KELLER-BOX SOLUTION OF THE STAGNATION POINT MICROPOLAR FLUID FLOW BETWEEN POROUS PLATES WITH INJECTION

The present study deals with the steady axisymmetric flow of micropolar fluid between two parallel porous plates when the fluid is injected through both walls at the same rate. The influence of velocity slip at the porous surface is analyzed. A detailed finite-difference solution is developed for the resulting non-linear coupled differential equations representing velocities and microrotation. The numerical computations are obtained for radial, axial velocities, and microrotation for varying injection Reynolds number, micropolar parameter, and slip coefficient. Further, a comparison of the results is given with those obtained in the literature with different methods as special cases.