An Ellam Scheme for Advection-Diffusion Equations in Two Dimensions

We develop an Eulerian{Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diusion 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

An ELLAM approximation for advective–dispersive transport with nonlinear sorption

We consider an Eulerian-Lagrangian localized adjoint method (ELLAM) applied to nonlinear model equations governing solute transport and sorption in porous media. Solute transport in the aqueous phase is modeled by standard advection and hydrodynamic dispersion processes, while sorption is modeled with a nonlinear local equilibrium model. We present our implementation of finite volume ELLAM (FV- ELLAM) and finite element (FE-ELLAM) discretizations to the reactive transport model and evaluate their performance for several test problems containing self- sharpening fronts