Initial-Boundary Layer Associated with the Nonlinear Darcy-Brinkman-Oberbeck-Boussinesq System
In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial-boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.
M. Fei et al., "Initial-Boundary Layer Associated with the Nonlinear Darcy-Brinkman-Oberbeck-Boussinesq System," Physica D: Nonlinear Phenomena, vol. 338, pp. 42 - 56, Elsevier, Jan 2017.
The definitive version is available at https://doi.org/10.1016/j.physd.2016.08.002
Mathematics and Statistics
Keywords and Phrases
Physics; Approximate solution; Boussinesq system; Darcy equations; Darcy number; Initial layer; Method of multiple scale; Optimal convergence; Singular perturbation problems; Boundary layers; Boundary layer; Darcy-Brinkman-Oberbeck-Boussinesq system; Initial layer; Initial-boundary layer; Vanishing Darcy number limit
International Standard Serial Number (ISSN)
Article - Journal
© 2017 Elsevier, All rights reserved.
01 Jan 2017