Professor Meriem Laleg's research on modeling contaminant transport published in SIAM Journal on Scientific Computing
A new algorithm is proposed to estimate the average velocity, dispersion coefficient, and differentiation order of a space-fractional advection-dispersion equation used for modeling contaminant transport in porous media. This allows for the characterization of the medium and the determination of the contaminant source. The algorithm is efficient, robust and fast.
About
In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.