Adjoint analysis of Buckley-Leverett and two-phase flow equations
Name
Jayasinghe_2018_Adjoint_Analysis_Buckley_Leverett.pdf
Description
Author's final manuscript
Size
1.57 MB
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Checksum (MD5)
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Author(s)
Burgess, Nicholas K.
Jayasinghe, Savithru
Darmofal, David L
Galbraith, Marshall C.
Allmaras, Steven R.
Date Issued
December 2017
Journal
Computational Geosciences
Publisher
Springer-Verlag
Citation
Jayasinghe, Savithru et al. “Adjoint Analysis of Buckley-Leverett and Two-Phase Flow Equations.” Computational Geosciences 22, 2 (January 2018): 527–542 © 2018 Springer International Publishing AG, part of Springer Nature
Version
Author's final manuscript
Abstract
This paper analyzes the adjoint equations and boundary conditions for porous media flow models, specifically the Buckley-Leverett equation, and the compressible two-phase flow equations in mass conservation form. An adjoint analysis of a general scalar hyperbolic conservation law whose primal solutions include a shock jump is initially presented, and the results are later specialized to the Buckley-Leverett equation. The non-convexity of the Buckley-Leverett flux function results in adjoint characteristics that are parallel to the shock front upstream of the shock and emerge from the shock front downstream of the shock. Thus, in contrast to the behavior of Burgers’ equation where the adjoint is continuous at a shock, the Buckley-Leverett adjoint, in general, contains a discontinuous jump across the shock. Discrete adjoint solutions from space-time discontinuous Galerkin finite element approximations of the Buckley-Leverett equation are shown to be consistent with the derived closed-form analytical solutions. Furthermore, a general result relating the adjoint equations for different (though equivalent) primal equations is used to relate the two-phase flow adjoints to the Buckley-Leverett adjoint. Adjoint solutions from space-time discontinuous Galerkin finite element approximations of the two-phase flow equations are observed to obey this relationship. Keywords: Adjoint solutions; Buckley-Leverett; Two-phase flow; Conservation law; Continuous analysis; Shockwaves
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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DOI of Published Version
https://doi.org/10.1007/s10596-017-9708-2
