# Analytical Solutions of One-dimensional Stokes' Problems for Infinite and Finite Domains with Generally Periodic Boundary Conditions (Contributo in atti di convegno)

- Type
- Contributo in atti di convegno (Classe)
- Prodotto della ricerca (Classe)

- Label
- Analytical Solutions of One-dimensional Stokes' Problems for Infinite and Finite Domains with Generally Periodic Boundary Conditions (Contributo in atti di convegno) (literal)

- Anno
- 2012-01-01T00:00:00+01:00 (literal)

- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
- 10.1063/1.4756653 (literal)

- Alternative label
- Durante, Danilo; Broglia, Riccardo (2012)(literal)
**Analytical Solutions of One-dimensional Stokes' Problems for Infinite and Finite Domains with Generally Periodic Boundary Conditions**

in International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2012, Kos; Greece, 19-25 September 2012

- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
- Durante, Danilo; Broglia, Riccardo (literal)

- Pagina inizio
- 2298 (literal)

- Pagina fine
- 2301 (literal)

- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
- http://dx.doi.org/10.1063/1.4756653 (literal)

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- 1479 (literal)

- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#volumeInCollana
- 1479 (literal)

- Rivista
- AIP conference proceedings (Rivista)

- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
- 4 (literal)

- Note
- ISI Web of Science (WOS) (literal)

- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- Consiglio Nazionale delle Ricerche (CNR) (literal)

- Titolo
- Analytical Solutions of One-dimensional Stokes' Problems for Infinite and Finite Domains with Generally Periodic Boundary Conditions (literal)

- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#isbn
- 978-0-7354-1091-6 (literal)

- Abstract
- The analysis of purely viscous unsteady flows, or Stokes' flow, consists in finding analytical solutions of parabolic equations (like the heat equation) for prescribed boundary conditions. Even if considered as an old-fashioned topic, the importance in solving this class of problems for different boundary conditions lies in the wide application fields in which they are encountered. Some actual and interesting problems, including the development of new materials, make the analysis of Stokes problems a fundamental topic; indeed, the flow over super-hydrophobic surfaces excellently modelled by a non-convective equation with mixed (homogeneous Dirichlet-homogeneous Neumann) boundary conditions (see for example [5], [9]). Ocean wave dynamics is another example: among others, [10] exploits simplified solutions of Stokes problems order to estimate the wave stress over the ocean bottom. The great interest for this solutions lies on the examination of the net mass transport phenomena associated to an ocean wave (Stokes' drift) generated by the wind in a rotating frame (see [4], [3], [8]). In the present work the Laplace transform in time is used in combination with the residuals theorem; once defined the path along which the complex integrals of the inverse transformation should be evaluated, this theorem allows straight deduction of the time and space dependent solution. As it will be demonstrated, in this way the analytical treatment of more general boundary conditions becomes possible. It will be also shown that by using the actual strategy, the introduction of a constant or sinusoidal pressure gradient offers only a slight complication which can be easily overtaken. Moreover the extension of the present solving technique to two dimensional problems avoids the onset of additional complications. In order to check the correctness of the computed analytical solutions, an algorithm which solves numerically differential problem has been implemented. The algorithm is based on a finite difference approximation of the Laplace operator for a generally non uniform distribution of the discretization points. (literal)

- Prodotto di
- Autore CNR
- DANILO DURANTE (Persona)
- RICCARDO BROGLIA (Persona)

- Insieme di parole chiave

#### Incoming links:

- Autore CNR di
- DANILO DURANTE (Persona)
- RICCARDO BROGLIA (Persona)

- Prodotto
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#rivistaDi
- AIP conference proceedings (Rivista)

- Insieme di parole chiave di