This paper describes a comparison of some numerical methods for solving the advection-diffusion (AD) equation which may be used to describe transport of a pollutant. The one-dimensional advection-diffusion equation is solved by using cubic splines (the natural cubic spline and a ”special” AD cubic spline) to estimate first and second derivatives, and also by solving the same problem using two s...

This paper provides a new fully discrete domain decomposition algorithm for the advection diffusion reaction equation. It relies on the optimized Ventcell–Schwarz algorithm with a finite volume discretization of the subdomain problems. The scheme includes a wide range of advection fluxes with a special treatment on the boundary. A complete analysis of the scheme is presented, and the convergenc...

We model the evolution of the concentration field of macromolecules in a symmetric field-flow fractionation (FFF) channel by a onedimensional advection-diffusion equation. The coefficients are precisely determined from the fluid dynamics. This model gives quantitative predictions of the time of elution of the molecules and the width in time of the concentration pulse. The model is rigorously su...

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...

We show that the solution of the Burgers equation can be approximated in LX(R), to within 0(m~1/*(lnm)2), by a random walk method generated by 0(m) particles. The nonlinear advection term of the equation is approximated by advecting the particles in a velocity field induced by the particles. The diffusive term is approximated by adding an appropriate random perturbation to the particle position...

Mass transport such as movement of phosphorus in soils and solutes in rivers is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or super diffusion and is well described using a fractional adv...

A new direct solution method for the advection-diffusion equation is presented. By employing a semi-implicit time discretisation, the equation is rewritten as a heat equation with source terms. The solution is obtained by discretely approximating the integral convolution of the associated Green’s function with advective source terms. The heat equation has an exponentially decaying Green’s funct...

Abstarct: Advection-diffusion equation with constant and variable coefficients has a wide range of practical and industrial applications. Due to the importance of advection-diffusion equation the present paper, solves and analyzes these problems using a new finite difference equation as well as a numerical scheme. The developed scheme is based on a mathematical combination between Siemieniuch a...