The Arnoldi reduction technique for efficient direct solution of radionuclide decay chain transport in dual-porosity media

An efficient technique is presented for the numerical solution of multi-spe cies radionuclide decay chain transport problems in dual-porosity media. Th e method is based on the Arnoldi modal reduction technique that uses orthog onal matrix transformations to reduce the discretized transport equations. The reduced equation system is much smaller than the original one. This new system can be solved by a standard Crank-Nicolson scheme with very little computational effort and then the original solutions at desired time steps are obtained by using a matrix-vector multiplication. In this paper, we als o develop two new alternative methods for choosing a common starting vector for all the transport species. The new methods can be used for most popula r cases of first or second type boundary conditions and ensure the converge nce of Arnoldi method. In addition, a new method for calculating mass excha nge between the matrix block and fracture is presented. This method calcula tes the leakage terms directly using reduced space data for both slab and s pherical matrix block and is highly efficient compared to the traditional i terative methods. The technique is verified through the comparison with ana lytical solutions. The efficiency and accuracy of the Arnoldi method are de monstrated by applying to the case study of three-species decay chain trans port in a heterogeneous dual-porosity aquifer system. The proposed techniqu e shows an impressive 98% saving in computing time and 75% saving in storag e space for the case study problem. The Arnoldi reduction method (ARM) affo rds an efficient means of solving large problems particularly when time dur ations are long or many species are involved. (C) 2000 Elsevier Science B.V . All rights reserved.