Abstract
The generalized Navier-Stokes equations for incompressible viscous flows through isotropic granular porous medium are considered. First Stokes problem is solved applying Laplace transform with respect to time variable and evaluating the inverse transform integrals by the residue calculus. The derived analytical solution includes the classic one as a particular case, that is, it can be obtained from the generalized solution by putting the porosity parameter equal to 1. The use of the derived exact solutions for benchmarking purposes is described.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bourchtein, A., Bourchtein, L., Lukaszczyk, J.P.: Numerical simulation of incompressible flows through granular porous media. Applied Numerical Mathematics 40 (2002) 291–306
Constantin, P., and Foias, C. Navier-Stokes equations. University of Chicago Press, Chicago (1989)
DuPlessis, P.J., and Masliyah, J.H.: Flow through isotropic granular porous media. Transport in Porous Media, 6 (1991) 207–221
Gradshteyn, I.S., Ryzhik, I.M.: Tables of integrals, series and products. Academic Press, Boston (1994)
Gresho, P.M.: Incompressible fluid dynamics: some fundamental formulation issues. Annual Reviews of Fluid Mechanics, 23 (1991) 413–453
Shilov, G.E.: Elementary real and complex analysis. Dover Publications, New York (1996)
Wang, C.Y.: Exact solutions of the unsteady Navier-Stokes equations. Applied Mechanics Review, 42 (1989) 269–282
Wang, C.Y.: Exact solutions of the steady-state Navier-Stokes equations. Annual Reviews of Fluid Mechanics, 23 (1991) 159–177
Yih, C.-S.: Fluid mechanics. McGraw-Hill, New York (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bourchtein, A., Bourchtein, L. (2002). Stokes Problem for the Generalized Navier-Stokes Equations. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47789-6_84
Download citation
DOI: https://doi.org/10.1007/3-540-47789-6_84
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43594-5
Online ISBN: 978-3-540-47789-1
eBook Packages: Springer Book Archive