New Second-Order Finite Difference Scheme for the Problem of Contaminant in Groundwater Flow

Abstract

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the $L^2$ norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite difference scheme.