Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

Vikram V Garg; Serge Prudhomme; Kris G van der Zee; Graham F Carey

doi:10.1186/s40323-014-0015-3

Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

Vikram V Garg, Serge Prudhomme, Kris G van der Zee, Graham F Carey

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Background Models based on the Helmholtz `slip' approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis. Methods We show that the direct formulation of the `slip' model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled `slip' model, which is shown to be well-posed, and therefore automatically adjoint-consistent. Results Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems. Conclusions An adjoint-consistent formulation for Helmholtz `slip' models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.

Original language	English (US)
Journal	Advanced Modeling and Simulation in Engineering Sciences
Volume	1
Issue number	1
DOIs	https://doi.org/10.1186/s40323-014-0015-3
State	Published - Sep 27 2014
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Vikram Garg is grateful for the support of the Bruton fellowship and the University Continuing fellowship from The University of Texas at Austin. Kris van der Zee is grateful for the support of this work by the 2010 NWO Innovational Research Incentives Scheme (IRIS) Grant 639.031.033. Serge Prudhomme is sponsored by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. Serge Prudhomme is also a participant of the KAUST SRI center for Uncertainty Quantification in Computational Science and Engineering.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems",

abstract = "Background Models based on the Helmholtz `slip' approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis. Methods We show that the direct formulation of the `slip' model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled `slip' model, which is shown to be well-posed, and therefore automatically adjoint-consistent. Results Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems. Conclusions An adjoint-consistent formulation for Helmholtz `slip' models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.",

author = "Garg, {Vikram V} and Serge Prudhomme and {van der Zee}, {Kris G} and Carey, {Graham F}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Vikram Garg is grateful for the support of the Bruton fellowship and the University Continuing fellowship from The University of Texas at Austin. Kris van der Zee is grateful for the support of this work by the 2010 NWO Innovational Research Incentives Scheme (IRIS) Grant 639.031.033. Serge Prudhomme is sponsored by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. Serge Prudhomme is also a participant of the KAUST SRI center for Uncertainty Quantification in Computational Science and Engineering. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1186/s40323-014-0015-3",

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AU - Garg, Vikram V

AU - Prudhomme, Serge

AU - van der Zee, Kris G

AU - Carey, Graham F

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Vikram Garg is grateful for the support of the Bruton fellowship and the University Continuing fellowship from The University of Texas at Austin. Kris van der Zee is grateful for the support of this work by the 2010 NWO Innovational Research Incentives Scheme (IRIS) Grant 639.031.033. Serge Prudhomme is sponsored by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. Serge Prudhomme is also a participant of the KAUST SRI center for Uncertainty Quantification in Computational Science and Engineering. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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Y1 - 2014/9/27

N2 - Background Models based on the Helmholtz `slip' approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis. Methods We show that the direct formulation of the `slip' model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled `slip' model, which is shown to be well-posed, and therefore automatically adjoint-consistent. Results Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems. Conclusions An adjoint-consistent formulation for Helmholtz `slip' models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.

AB - Background Models based on the Helmholtz `slip' approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis. Methods We show that the direct formulation of the `slip' model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled `slip' model, which is shown to be well-posed, and therefore automatically adjoint-consistent. Results Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems. Conclusions An adjoint-consistent formulation for Helmholtz `slip' models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.

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Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

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