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Development of a High-Resolution Scheme for Solving the PNP-NS Equations in Curved Channels

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Incompressible viscous fluids

Published online by Cambridge University Press:  01 February 2016

Tony W. H. Sheu ,
Yogesh G. Bhumkar ,
S. T. Yuan  and
S. C. Syue
Tony W. H. Sheu*
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan, 10617 Center of Advanced Study in Theoretical Sciences (CASTS), National Taiwan University, Taipei, Taiwan, 10617 Institute of Applied Mathematical Sciences, National Taiwan University, Taipei, Taiwan, 10617
Yogesh G. Bhumkar
Affiliation:
Center of Advanced Study in Theoretical Sciences (CASTS), National Taiwan University, Taipei, Taiwan, 10617 School of Mechanical Sciences, IIT Bhubaneswar, Odisha, India751013
S. T. Yuan
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan, 10617
S. C. Syue
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan, 10617
*
*Corresponding author. Email addresses:twhsheu@ntu.edu.tw (T. W. H. Sheu), bhumkaryogesh@gmail.com (Y. G. Bhumkar), r99525055@ntu.edu.tw (S. T. Yuan), r02525068@ntu.edu.tw (S. C. Syue)
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Abstract

A high-order finite difference scheme has been developed to approximate the spatial derivative terms present in the unsteady Poisson-Nernst-Planck (PNP) equations and incompressible Navier-Stokes (NS) equations. Near the wall the sharp solution profiles are resolved by using the combined compact difference (CCD) scheme developed in five-point stencil. This CCD scheme has a sixth-order accuracy for the second-order derivative terms while a seventh-order accuracy for the first-order derivative terms. PNP-NS equations have been also transformed to the curvilinear coordinate system to study the effects of channel shapes on the development of electroos-motic flow. In this study, the developed scheme has been analyzed rigorously through the modified equation analysis. In addition, the developed method has been computationally verified through four problems which are amenable to their own exact solutions. The electroosmotic flow details in planar and wavy channels have been explored with the emphasis on the formation of Coulomb force. Significance of different forces resulting from the pressure gradient, diffusion and Coulomb origins on the convective electroosmotic flow motion is also investigated in detail.

Keywords

PNPNSfive-point stencilcombined compact differenceelectroosmotic flowCoulomb force

MSC classification

Secondary: 76D05: Navier-Stokes equations 76D55: Flow control and optimization 65M06: Finite difference methods 65M22: Solution of discretized equations
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 496 - 533
Copyright
Copyright © Global-Science Press 2016 

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