Exponential finite difference scheme for transport equations with discontinuous coefficients in porous media

Tatiana P. Chernogorova, Miglena N. Koleva and Lubin G. Vulkov

Applied Mathematics and Computation, 2021, vol. 392, issue C

Abstract: In this paper, we propose a novel exponential difference scheme for solving non-linear problems arising in variably saturated flow with discontinuous absolute permeability. First, we derive the discretization for a linear convection-diffusion-reaction problem with discontinuous coefficients. Positivity preserving property, stability and convergence of the scheme are studied. Then, the method is implemented to the transport equation and Richards’ equation. Various numerical experiments on graded and uniform meshes are presented and discussed.

Keywords: Exponential difference scheme; Interface problems; Positivity preserving; Richards’ equation; Transport equation; Discontinuous coefficients; Stability; Convergence (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306445

DOI: 10.1016/j.amc.2020.125691

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