NUMERICAL ADVECTION EXPERIMENTS1

A numerical scheme for space-time fractional advection-dispersion equation

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

Numerical Solution of Advection-Diffusion-Reaction Equations

Numerical Algorithms 0 ( 1998 ) ? { ? 1 A Hybrid Nonoverlapping Domain DecompositionScheme for Advection Dominated Advection - Di usionProblems

Two nonoverlapping domain decomposition algorithmsare proposed for convectiondom-inated convection-diiusion problems. In each subdomain, artiicial boundary conditions are used on the innow and outtow boundaries. If the ow is simple, each subdomain problem only needs to be solved once. If there are closed streamlines, an iterative algorithmis needed and the convergence is proved. Analysis and nu...

Numerical Solving Two-dimensional Variable-order Fractional Advection-dispersion Equation

Abstract: In this paper, a two-dimensional variable-order fractional advection-dispersion equation with variable coefficient is considered. The numerical method with first order temporal accuracy and first order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by using energy method. Finally, the results of a numerical example supports the theoret...

A numerical scheme for space-time fractional advection-dispersion equation

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the evaluation of the terms involving spatial fractional order derivatives. Then utilizing Bernstein polynomials as basis, the problem is transformed into a linear ...