An Eulerian-Lagrangian Localized Adjoint Method for Advection-dispersion Equations in Two Dimensions and Its Comparison to Other Schemes
University of South Carolina Columbia
Pagination or Media Count:
We develop an ELLAM Eulerian-Lagrangian localized adjoint method scheme to solve two-dimensional advection-dispersion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate the strength of the ELLAM scheme.