Lanczos method for the solution of groundwater flow in discretely fractured porous media

One of the more advanced approaches for simulating groundwater flow in frac tured porous media is the discrete-fracture approach. This approach is limi ted by the large computational overheads associated with traditional modeli ng methods. In this work, we apply the Lanczos reduction method to the mode ling of groundwater flow in fractured porous media using the discrete-fract ure approach. The Lanczos reduction method reduces a finite element equatio n system to a much smaller tridiagonal system of first-order differential e quations. The reduced system can be solved by a standard tridiagonal algori thm with little computational effort. Because solving the reduced system is more efficient compared to solving the original system, the simulation of groundwater flow in discretely fractured media using the reduction method i s very efficient. The proposed method is especially suitable for the proble m of large-scale and long-term simulation. In this paper, we develop an ite rative version of Lanczos algorithm, in which the preconditioned conjugate gradient solver based on ORTHOMIN acceleration is employed within the Lancz os reduction process. Additional efficiency for the Lanczos method is achie ved by applying an eigenvalue shift technique. The "shift" method can impro ve the Lanczos system convergence, by requiring fewer modes to achieve the same level of accuracy over the unshifted case. The developed model is veri fied by comparison with dual-porosity approach. The efficiency and accuracy of the method are demonstrated on a field-scale problem and compared to th e performance of classic time marching method using an iterative solver on the original system. In spite of the advances, more theoretical work needs to be carried out to determine the optimal value of the shift before comput ations are actually carried out. (C) 2001 Elsevier Science Ltd. All rights reserved.