A numerical simulation of chemical contaminant transport problems in inhomogeneous media using a 2D-TFDCR model

Abstract

Problems that are assumed to be relevant for anisotropic inhomogeneous media and governed by a Caputo time fractional diffusion-convection-reaction equation (TFDCRE) of a class of time-space variable coefficients, are considered. First, the time-space variable coefficient equation is transformed into a time variable coefficient equation. Then, by using the Gauss divergence theorem and the convolution theorem of Laplace transform , the time variable coefficients equation is converted into a boundary integral equation, for which a standard boundary element method (BEM) is applied to find numerical solutions in the frame of the Laplace transform. The numerical solutions are then inverted using the Stehfest method to obtain solutions in the original time variable. Some problems with trigonometric, exponential, and quadratic spatial gradation function coefficients have been solved. The validity of the analysis used to derive the boundary integral equation is verified, the BEM solutions are convergent and accurate. Additionally, the effects of the anisotropy and variabilities of the coefficients are demonstrated. It is evident that the order of the fractional derivative has a damping-like effect on the system.

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