Application of the Lanczos algorithm to the simulation of groundwater flowin dual-porosity media

Groundwater flow in fractured porous media can be realistically described u sing a dual-porosity approach. A popular numerical approach for simulation of groundwater flow in dual-porosity media is the use of spatial discretiza tion procedures based upon the finite element techniques. The computational effort for this technique strongly depends on both the number of unknowns and the number of time steps required to obtain an accurate and stable solu tion. In this paper we develop a modal decomposition technique based on the Lanczos algorithm to solve the equations of transient groundwater flow in fractured dual-porosity media. The Lanczos algorithm uses orthogonal matrix transformations to reduce the finite element equations to a much smaller t ridiagonal system of first-order differential equations. By using this meth od, problems with large node number can be reduced into equivalent systems of much smaller size. Consequently, large savings in computer time can be r ealized, especially for the problems requiring many time steps. The efficie ncy is further achieved by using a recursion method to compute the fluid ex change between matrix blocks and fractures. In addition, this paper shows h ow time-dependent boundary conditions or multiple sources or sinks can be r ealized for the Lanczos method. In order to verify the proposed numerical t echnique and show its efficiency, two examples are presented: one is for a homogeneous aquifer and the results are compared to the analytical solution s and the other shows a multiple well system of different time histories in a synthetic dual-porosity aquifer. (C) 2000 Elsevier Science Ltd. All righ ts reserved.