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 superdiffusion, and it is well described using a fractiona...

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

where a(x, t) is some scalar quantity and u is the velocity at which it is advected (u > 0 advects to the right). The solution to Eq. 1 is to simply take the initial data, a(x, t = 0), and displace it to the right at a speed u. The shape of the initial data is preserved in the advection. Many hyperbolic systems of PDEs, e.g. the equations of hydrodynamics, can be written in a form that looks li...

The mathematical properties of a nonlinear parabolic equation arising in the modelling of non-newtonian flows are investigated. The peculiarity of this equation is that it may degenerate into a hyperbolic equation (in fact a linear advection equation). Depending on the initial data, at least two situations can be encountered: the equation may have a unique solution in a convenient class, or it ...

We show a superconvergence property for the Semi-Lagrangian Discontinuous Galerkin scheme of arbitrary degree in the case of constant linear advection equation with periodic boundary conditions.

This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of...

We analyze a space-time domain decomposition iteration, for a model advection diiusion equation in one and two dimensions. The asymptotic convergence rate is superlinear, and it is governed by the diiusion of the error across the overlap between subdomains. Hence, it depends on both the size of this overlap and the diiusion coeecient in the equation. However, it is independent of the number of ...

Despite the growing popularity of Lattice Boltzmann schemes for describing multi-dimensional flow and transport governed by non-linear (anisotropic) advectiondiffusion equations, there are very few analytical results on their stability, even for the isotropic linear equation. In this paper, the optimal two-relaxation-time (OTRT) model is defined, along with necessary and sufficient (easy to use...

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. ...

Mathematical models for pollutant transport in semi-infinite aquifers are based on the advection-dispersion equation (ADE) and its variants. This study employs the ADE incorporating time-dependent dispersion and velocity and space-time dependent source and sink, expressed by one function. The dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity. Initial...