A Residual Theorem Approach Applied to Stokes’ Problems with Generally Periodic Boundary Conditions including a Pressure Gradient Term
Joint Authors
Durante, Danilo
Broglia, Riccardo
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-08-28
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
The differential problem given by a parabolic equation describing the purely viscous flow generated by a constant or an oscillating motion of a boundary is the well-known Stokes’ problem.
The one-dimensional equation is generally solved for unbounded or bounded domains; for the latter, either free slip (i.e., zero normal gradient) or no-slip (i.e., zero velocity) conditions are enforced on one boundary.
Generally, the analytical strategy to solve these problems is based on finding the solutions of the Laplace-transformed (in time) equation and on inverting these solutions.
In the present paper this problem is solved by making use of the residuals theorem; as it will be shown, this strategy allows achieving the solutions of First and Second Stokes’ problems in both infinite and finite depth.
The extension to generally periodic boundaries with the presence of a periodic pressure gradient is also presented.
This approach allows getting closed form solutions in the time domain in a rather fast and simple way.
An ad hoc numerical algorithm, based on a finite difference approximation of the differential equation, has been developed to check the correctness of the analytical solutions.
American Psychological Association (APA)
Durante, Danilo& Broglia, Riccardo. 2018. A Residual Theorem Approach Applied to Stokes’ Problems with Generally Periodic Boundary Conditions including a Pressure Gradient Term. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1205539
Modern Language Association (MLA)
Durante, Danilo& Broglia, Riccardo. A Residual Theorem Approach Applied to Stokes’ Problems with Generally Periodic Boundary Conditions including a Pressure Gradient Term. Mathematical Problems in Engineering No. 2018 (2018), pp.1-16.
https://search.emarefa.net/detail/BIM-1205539
American Medical Association (AMA)
Durante, Danilo& Broglia, Riccardo. A Residual Theorem Approach Applied to Stokes’ Problems with Generally Periodic Boundary Conditions including a Pressure Gradient Term. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1205539
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1205539