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EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Citation:
Celia, M., T. Russell, I. Herrera, AND R. Ewing. EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION. U.S. Environmental Protection Agency, Washington, D.C., EPA/600/J-90/444 (NTIS PB91177253), 1990.
Description:
Many numerical methods use characteristic analysis to accommodate the advective component of transport. uch characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. eneralization of characteristic methods can be developed using an approach that we refer to as an Eulerian-Lagrangian localized adjoint method (ELLAM). his approach is a space-time extension of the optimal test function (OTT) method. he method provides a consistent formulation by defining test functions as specific solutions of the localized homogeneous adjoint equation. ll relevant boundary terms arise naturally in the ELLAM formulation, and a systematic and complete treatment of boundary condition implementation results. his turns out to have significant implications for the calculation of boundary fluxes. An analysis of global mass conservation leads to the final ELLAM approximation, which is shown to possess the conservative property. umerical calculations demonstrate the behavior of the method with emphasis on treatment of boundary conditions. iscussion of the method includes ideas on extensions to higher spatial dimensions, reactive transport, and variable coefficient equations.
