Numerical solutions for solute transport in unconfined aquifers

Abstract

SUMMARYTwo numerical methods for solving the problem of solute transport in unsteady flow in unconfined aquifers are studied. They are the method of characteristics (MOC) based on the finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into four schemes: moving mesh, pseudo-Lagrangian (FEM1); stationary mesh, pseudo-Lagrangian (FEM2); pseudo saturated-unsaturated, Eulerian (FEM3); and non-stationary element, Eulerian (FEM4).Experiments on a one-dimensional flow case are performed to illustrate the schemes and to determine the effect of discretization on accuracy. In two-dimensional flow the above methods are compared with experimental results from a sand box model. Results indicate that for a similar degree of accuracy, the FEM requires less computational effort than the MOC. Among the four FEM schemes, FEM4 appears to be most attractive as it is the most efficient and most convenient to apply.

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

“…The partial differential advection-diffusion equation (ADE) describes water transfer in soils (Parlange, 1980), dispersion of tracers in porous media (Fattah and Hoopes, 1985), the spread of pollutants in rivers and streams (Chatwin and Allen, 1985), the dispersion of dissolved material in estuaries and coastal seas (Holly and Usseglio-Polatera, 1984), contaminant dispersion in shallow lakes (Salmon et al, 1980), the absorption of chemicals into beds (Lapidus and Amundston, 1952), long-range transport of pollutants in the atmosphere (Zlatev et al, 1984), forced cooling by fluids of solid material such as windings in turbo generators (Gane and Stephenson, 1979), thermal pollution in river systems (Chaudhry et al, 1983), flow in porous media (Kumar, 1988) and dispersion of dissolved salts in groundwater (Guvanasen and Volker, 1983). Logan and Zlotnik (1995) proposed analytical solutions with a decay term for periodic input conditions through a semiinfinite domain to address fluctuations of the groundwater table and flow patterns caused by the periodicity of the sea level.…”

A compact unconditionally stable finite‐difference method for transient one‐dimensional advection‐diffusion

“…''-I2 All of these methods involve a spread of at least three grid points in space except those of Holly and Preissmann, l 3 Lam and Simpson, l4 and von Rosenberg, l5 which use only two spatial grid points. However, the first two of these methods require the solution of an additional equation at each grid point for the computation of the spatial gradient of i , have a derivative boundary condition at x = 0 replacing condition (4) and require initial values of the spatial gradient to be given in addition to (2). The third method has only restricted application because it requires the Courant number to have the fixed value of 1.…”

Comparative study of some numerical methods to solve a 3D advection-diffusion equation

“…It has been used to describe heat transfer in a draining film [1], mass transfer [2], flow in porous media [3] and charge transport in semi-conductor devices [4]. The 3D advection-diffusion equation is given by: ∂u ∂t + β x ∂u ∂x + β y ∂u ∂y + β z ∂u ∂z = α x ∂ 2 u ∂x 2 + α y…”