TY - EJOU
AU - Liu, Chein-Shan
AU - Chang, Chih-Wen
AU - Chang, Jiang-Ren
TI - A Quasi-Boundary Semi-Analytical Method for Backward in Time Advection-Dispersion Equation
T2 - Computers, Materials \& Continua
PY - 2009
VL - 9
IS - 2
SN - 1546-2226
AB - In this paper, we take the advantage of an analytical method to solve the advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is employed to calculate the concentration field *C(x, t)* at any time *t< T*. Then, we consider a direct regularization by adding an extra term *αC(x,0)* on the ﬁnal condition to carry off a second kind Fredholm integral equation. The termwise separable property of the kernel function permits us to transform itinto a two-point boundary value problem. The uniform convergence and error estimate of the regularized solution *C*^{α}(x,t) are provided and a strategy to select the regularized parameter is suggested. The solver used in this work can recover the spatial distribution of the groundwater contaminant concentration. Several numerical examples are examined to show that the new approach can retrieve all past data very well and is good enough to cope with heterogeneous parameters’ problems, even though the ﬁnal data are noised seriously.
KW - Inverse problem
KW - Groundwater contaminant distribution
KW - Advection-dispersion equation
KW - Fredholm integral equation
KW - Two-point boundary value problem
DO - 10.3970/cmc.2009.009.111