Abstract: Solving or approximating the advection-diffusion/dispersion equation (ADE) is a challenging and important problem and has thus motivated a great deal of intense research. A specific complication arises from the nature of the governing partial differential equation: it is characterized by a hyperbolic non-dissipative advective transport term, a parabolic dissipative diffusive (dispersi...

Lattice Boltzmann Methods (LBMs) are relatively new and have not yet been widely applied to ground-water systems. LBMs are particularly attractive for numerical modeling of flow and solute transport in karst aquifers because they are able to: • Simulate inertial flows • Incorporate complex wall and conduit geometries • Solve adjacent Darcian and Navier-Stokes flow regimes • Solve the appropriat...

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

We consider the problem of numerically approximating the solution of the coupling of the flow equation in a porous medium, with the advection-diffusion equation in the presence of uncertainty on the permeability of the medium. Random coefficients are classically used in the flow equation to modelize uncertainty. More precisely, we propose the numerical analysis of a method developed to compute ...

Solute transport through regional-scale fractured rocks and heterogeneous porous media typically exhibits several “anomalous” features including 1) different growth rates along different directions, due to an anisotropic depositional or structural geologic environment; and 2) channeling along preferential flow paths. Simulating such plume characteristics can be computationally intensive using a...