Finite difference approximations for fractional advection-dispersion flow equations. (English) Zbl 1126.76346

Meerschaert, Mark M.; Tadjeran, Charles

J. Comput. Appl. Math. 172, No. 1, 65-77 (2004).

Summary: Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper we develop practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain. The practical application of these results is illustrated by modeling a radial flow problem. Use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site.

MSC:

76M20	Finite difference methods applied to problems in fluid mechanics
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
26A33	Fractional derivatives and integrals
35Q35	PDEs in connection with fluid mechanics
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Finite difference approximation; Stability; Backward Euler method; Implicit Euler method; Radial dispersion; Radial advection; Fractional diffusion; Fractional derivative; Fractional advection–dispersion; Numerical fractional ADE

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