TY - JOUR
T1 - An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation
AU - Celia, Michael Anthony
AU - Russell, Thomas F.
AU - Herrera, Ismael
AU - Ewing, Richard E.
N1 - Funding Information:
Although the research described in this article has been funded in part by the U.S. Environmental Protection Agency, it has not been subjected to Agency review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.
Funding Information:
through NSF Grant No. RII-8610680, and by the EnvironmentaPl rotectionA gency under AssistanceA gree-ment CR 814945 to Princeton University. The authors gratefully acknowledge the assistanceo f Simon Zisman in preparing the manuscript.
Funding Information:
This work wass upporteidn partb y theN ationaSl cience Foundation under Grants 8657419-CES and DMS-8821330b,y theI nstitutfeo r ScientificC omputing
PY - 1990/12
Y1 - 1990/12
N2 - Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteristic methods can be developed using an approach that we refer to as an Eulerian-Lagrangian localized adjoint method (ELLAM). This approach is a space-time extension of the optimal test function (OTF) method. The method provides a consistent formulation by defining test functions as specific solutions of the localized homogeneous adjoint equation. All relevant boundary terms arise naturally in the ELLAM formulation, and a systematic and complete treatment of boundary condition implementation results. This 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. Numerical calculations demonstrate the behaviour of the method with emphasis on treatment of boundary conditions. Discussion of the method includes ideas on extensions to higher spatial dimensions, reactive transport, and variable coefficient equations.
AB - Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteristic methods can be developed using an approach that we refer to as an Eulerian-Lagrangian localized adjoint method (ELLAM). This approach is a space-time extension of the optimal test function (OTF) method. The method provides a consistent formulation by defining test functions as specific solutions of the localized homogeneous adjoint equation. All relevant boundary terms arise naturally in the ELLAM formulation, and a systematic and complete treatment of boundary condition implementation results. This 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. Numerical calculations demonstrate the behaviour of the method with emphasis on treatment of boundary conditions. Discussion of the method includes ideas on extensions to higher spatial dimensions, reactive transport, and variable coefficient equations.
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U2 - 10.1016/0309-1708(90)90041-2
DO - 10.1016/0309-1708(90)90041-2
M3 - Article
AN - SCOPUS:0025639748
SN - 0309-1708
VL - 13
SP - 187
EP - 206
JO - Advances in Water Resources
JF - Advances in Water Resources
IS - 4
ER -