Development of a High-Resolution Scheme for Solving the PNP-NS Equations in Curved Channels (Communications in Computational Physics, 2018)
A high-order finite difference scheme has been developed to approximatethe spatial derivative terms present in the unsteady Poisson-Nernst-Planck (PNP) equationsand incompressible Navier-Stokes (NS) equations. Near the wall the sharp solutionprofiles are resolved by using the combined compact difference (CCD) schemedeveloped in five-point stencil. This CCD scheme has a sixth-order accuracy for thesecond-order derivative terms while a seventh-order accuracy for the first-order derivativeterms. PNP-NS equations have been also transformed to the curvilinear coordinatesystem to study the effects of channel shapes on the development of electroosmoticflow. In this study, the developed scheme has been analyzed rigorously throughthe modified equation analysis. In addition, the developed method has been computationallyverified through four problems which are amenable to their own exact solutions.The electroosmotic flow details in planar and wavy channels have been exploredwith the emphasis on the formation of Coulomb force. Significance of different forcesresulting from the pressure gradient, diffusion and Coulomb origins on the convectiveelectroosmotic flow motion is also investigated in detail.