Numerical modelling of mass transport in hydrogeologic environments: performance comparison of the Laplace Transform Galerkin and Arnoldi modal reduction schemes

Abstract

The Laplace Transform Galerkin (LTG) method and the Arnoldi modal reduction method (AMRM) have been implemented in finite element schemes designed to solve mass transport problems in porous media by Sudicky [Sudicky, E.A., Water Resour. Res., 25(8) (1989) 1833-46] and Woodbury et al [Woodbury, A.D., Dunbar, W.S., & Nour-Omid, B., Water Resour. Res., 26(10) (1990) 2579-90]. In this work, a comparative analysis of the two methods is performed with attention focused on efficiency and accuracy. The analysis is performed over one- and two-dimensional domains composed of homogeneous and heterogeneous material properties. The results obtained using homogeneous material properties indicate that for a given mesh design the LTG method maintains a higher degree of accuracy than does the AMRM. However, in terms of efficiency, the Arnoldi attains a pre-defined level of accuracy faster than does the LTG method. It is also shown that for problems involving homogeneous material properties the solution obtained using the LTG method on a coarse mesh is comparable in terms of solution time and accuracy to that obtained using the AMRM on a fine mesh. Comparisons similar to those performed using homogeneous material properties are also performed for the case where the hydraulic conductivity field is heterogeneous. For this case, the level of accuracy achieved by the AMRM and the LTG method are similar. However, as with the analysis involving homogeneous material properties, the AMRM is found to be more efficient than the LTG method. It is also shown that for heterogeneous material properties, use of the LTG method under high grid Peclet conditions can be potentially problematic.