A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Advection-Dispersion Equation
Chih-Wen Chang1, Chein-Shan Liu2
CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 19-40, 2010, DOI:10.3970/cmc.2010.017.019
Abstract In this study, we employ a semi-analytical approach to solve a two-dimensional advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is used to calculate the concentration field C(x, y, t) at any time t < T. Then, we ponder a direct regularization by adding an extra termaC(x, y, 0) on the final time data C(x, y, T), to reach a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us obtaining a closed-form solution of the Fourier coefficients. A strategy to choose the regularization parameter is More >