A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction.
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Authors
LaFleur, Anthony
Issue Date
2014
Type
Thesis
Language
Keywords
Characteristic , Finite Difference , Fractional Calculus
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Abstract
Contaminant transport in porous media can be modeled with fractional differential equations. This approach results in early arrival of contaminants and heavy-tail distributions observed in field experiments. The implicit finite difference scheme with the shifted Grunwald approximation discritizing the fractional advection-diffusion equation unconditionally stable. We add an additional non-linear, Lipschitz continuous term to account for reactions and we solve the advection-diffusion equation utilizing fast Toeplitz matrix-vector multiplication. We then extend the method to the two-dimensional case. Numerical results are provided to compare performance of the methods proposed.
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In Copyright(All Rights Reserved)