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Finite element transport modeling using analytic element flow solutions
Author(s) -
Craig J. R.,
Rabideau A. J.
Publication year - 2006
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2005wr004695
Subject(s) - finite element method , discretization , classification of discontinuities , flow (mathematics) , method of mean weighted residuals , extended finite element method , mixed finite element method , mathematics , boundary (topology) , mathematical analysis , boundary value problem , mathematical optimization , geometry , galerkin method , engineering , structural engineering
Finite element methods for solute transport simulation typically use a discrete representation of the flow domain obtained from a finite element solution of the associated groundwater flow problem. Velocity, saturated thickness, and components of the dispersion coefficient tensor are represented as a set of nodal and/or element‐averaged values. In contrast, the analytic element method (AEM) provides continuous mesh‐independent solutions for these variables. In this paper, a set of techniques for using two‐dimensional AEM flow solutions as the basis of finite element solute transport models is introduced. First, a general AEM‐based discretization approach is presented that addresses the existence of curved boundaries, singularities, and discontinuities in vertically averaged concentration. Second, residual integration methods that handle continuous parameters with internal and boundary singularities are developed and evaluated. Third, an approach is introduced for handling internal discontinuities in concentration across certain analytic elements. This new approach uses a nonstandard mesh topology and a new formulation for internal coupled boundary conditions. The AEM‐based transport simulation methods introduced in this paper are demonstrated to be robust and accurate for a variety of test problems.