Abstract
We investigate viscous boundary layers of the plane-parallel flow, governed by the stationary Navier–Stokes equations under a certain symmetry. Following the analysis in Gie et al. (Annales de l’Institut Henri Poincaré C. Analyse Non Linéaire, 2018), we first construct the so-called corrector, which is an analytic approximation of the velocity vector field near the boundary. Then, by embedding the corrector function into the classical Finite Volume schemes, we construct the semi-analytic enriched Finite Volume schemes for the plane-parallel flow, and numerically verify that our new enriched schemes reduce significantly the computational error of classical schemes especially near the boundary, and hence produce more accurate approximations without introducing any finer mesh near the boundary.
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Acknowledgements
The first author was supported partially by Collaboration Grant for Mathematicians, Simons Foundation and Research - RII Grant, Office of the Executive Vice President for Research and Innovation, University of Louisville. The second and third authors were supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (2018R1D1A1B07048325) and the Research Fund (1.190136.01) of UNIST.
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Gie, GM., Jung, CY. & Lee, H. Enriched Finite Volume Approximations of the Plane-Parallel Flow at a Small Viscosity. J Sci Comput 84, 7 (2020). https://doi.org/10.1007/s10915-020-01259-0
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DOI: https://doi.org/10.1007/s10915-020-01259-0