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

Groundwater ̄ow in fractured porous media can be realistically described using a dual-porosity approach. A popular numerical approach for simulation of groundwater ̄ow in dual-porosity media is the use of spatial discretization procedures based upon the ®nite element techniques. The computational e€ort for this technique strongly depends on both the number of unknowns and the number of time steps required to obtain an accurate and stable solution. In this paper we develop a modal decomposition technique based on the Lanczos algorithm to solve the equations of transient groundwater ̄ow in fractured dual-porosity media. The Lanczos algorithm uses orthogonal matrix transformations to reduce the ®nite element equations to a much smaller tridiagonal system of ®rst-order di€erential equations. By using this method, problems with large node number can be reduced into equivalent systems of much smaller size. Consequently, large savings in computer time can be realized, especially for the problems requiring many time steps. The eciency is further achieved by using a recursion method to compute the ̄uid exchange between matrix blocks and fractures. In addition, this paper shows how time-dependent boundary conditions or multiple sources or sinks can be realized for the Lanczos method. In order to verify the proposed numerical technique and show its eciency, two examples are presented: one is for a homogeneous aquifer and the results are compared to the analytical solutions and the other shows a multiple well system of di€erent time histories in a synthetic dual-porosity aquifer. Ó 2000 Elsevier Science Ltd. All rights reserved.