||Eulerian-Lagrangian Localized Adjoint Method for the Advection-Diffusion Equation.
Celia, M. A. ;
Russell, T. F. ;
Herera, I. ;
Ewing, R. E. ;
||Princeton Univ., NJ. Dept. of Civil Engineering and Operations Research. ;Colorado Univ. at Denver. Dept. of Mathematics. ;Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Geofisica.;Robert S. Kerr Environmental Research Lab., Ada, OK.;National Science Foundation, Washington, DC.
Transport theory ;
Diffusion theory ;
Numerical solution ;
Localized adjoint methods
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The paper presents a space-time localized adjoint method (LAM) approximation for the advection-diffusion transport equation. The formulation is based on a space-time discretization in which specialized test functions are defined. These functions locally satisfy the homogeneous adjoint equation within each element. The formulation leads to a general approximation that subsumes many specific methods based on combined Lagrangian and Eulerian approaches, so-called characteristic methods (CM's). The authors refer to the method as an Eulerian-Lagrangian localized adjoint method (ELLAM). The ELLAM approach not only provides a unification of CM methods, but also provides a systematic framework for incorporation of boundary conditions in CM approximations. Example calculations were presented to demonstrate that the ELLAM procedure can handle all types of boundary conditions.