We define a family of discrete Advection-reaction operators, denoted by Aaλ, which associate to a given scalar sequence s = {sn} the sequence given by Aaλ(s) ≡ {bn}, where bn = an−2sn−1 + λnsn for n = 1, 2, . . .. For Aaλ we explicitly find their iterates and study their convergence properties. Finally, we show the relationship between the family of discrete operators with the continuous one di...

We analyze the convergence behavior of the overlapping Schwarz waveform relaxation algorithm applied to nonlinear advection problems. We show for Burgers’ equation that the algorithm converges super-linearly at a rate which is asymptotically comparable to the rate of the algorithm applied to linear advection problems. The convergence rate depends on the overlap and the length of the time interv...

Time-dependent advection-diffusion equations arise in mathematical models of porous medium flow and transport processes, including petroleum reservoir simulation, environmental modeling, and other applications. In such applications as immiscible displacement of oil by water in a secondary oil recovery process in petroleum industry or a groundwater transport process involving a non-aqueous phase...

A numerical model for electro-osmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier–Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences are second-order accurate and centered in space; however, the traditional second-order compact finite differen...

A non-traditional operator split (OS) scheme for the solution of the advection-diffusion-reaction (ADR) equation is proposed. The scheme is implemented with the recently published central scheme [A. Kurganov, E. Tadmor, New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000) 241–282] to accurately simulate advection-re...

Previous work showed how moving particles that rest along their trajectory lead to timenonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions...

A numerical model is presented for computation of unsteady two-fluid interfaces in nonlinear porous media flow. The nonlinear Forchheimer equation is included in the Navier-Stokes equations for porous media flow. The model is based on capturing the interface on a fixed mesh domain. The zero level set of a pseudo-concentration function, which defines the interface between the two fluids, is gove...

A parallel time integration method for nonlinear partial differential equations is proposed. It is based on a new implementation of the Paraexp method for linear partial differential equations (PDEs) employing a block Krylov subspace method. For nonlinear PDEs the algorithm is based on our Paraexp implementation within a waveform relaxation. The initial value problem is solved iteratively on a ...

In the present paper Haar wavelet method is implemented on advectiondispersion equation representing one dimensional contaminant transport through a porous medium. Non uniform flow is considered by assuming velocity and dispersion varying with time as an exponentially increasing function. Expressing the Haar wavelets in advection-dispersion equation into Haar series provides the main advantage ...

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...