Abstract
A finite element model of the flow in the Bosphorus strait based on the shallow water equations is presented. The Petrov-Galerkin approach is used for spatial discretization. An unstructured grid with linear triangular elements is employed. Integration of the resulting ordinary differential equation system with respect to time is based on the implicit trapezoidal rule. The advection-diffusion equation for the contaminant transport is solved similarly. The results are compared with in situ measurement values. It is concluded that the shallow water model is a very practical tool to study the contaminant transport in the Bosphorus strait even though the actual flow field includes density counter currents in the lower levels, necessitating a true 3-D model to be represented.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Abraham G., van Os A. G. and Verboom G. K. (1981): Transport models for inland and coastal waters. H. B. Fischer ed., Academic Press, 1–38
Brooks A. N. and Hughes T. J. R. (1982): Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comp. Meth. in App. Mech. and Eng., 32, 199–259
Connor J. and Wang J. (1974): Finite element modelling of hydrodynamic circulation. Numerical methods in fluid dynamics, Brebbia and Connor eds., Pentech Press, 355–387
Gray W. G. (1984): On normal flow boundary conditions in finite element codes for two-dimensional shallow water flow. Int. J. for Num. Meth. in Fluids, 4, 99–104
Gustafsson B. and Sundström A. (1978): Incompletely parabolic problems in fluid dynamics. SIAM J. Appl. Math., 35, 343–357
Kashiyama K., Ito H., Behr M. and Tezduyar T. (1994): Three-step explicit finite element computation of shallow water flows on a massively parallel computer. AHPCRC 94-055 preprint
Kawahara M. and Kashiyama K. (1984): Selective lumping finite element method for nearshore current. Int. J. for Num. Meth. in Fluids, 4, 71–97
King I. P., Norton W. R. and Iceman K. R. (1974): A finite element solution for two-dimensional stratified flow problems. Finite elements in fluids, vol. 1, 133–156, Gallagher et al. eds., Wiley
Örs H. and Aydm C. (1993): A numerical model of the circulation in Haliç, Antalya V. Milli Mek. Kong.
Saad Y. and Schultz M. (1986): GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. and Sta. Comp., 7, 856–869
Taylor C. and Davis J. M. (1974): Tidal propagation and dispersion estuaries. Finite elements in fluids, vol. 1, 95–118, Gallagher et al eds., Wiley
Zienkiewicz O. C. and Heinrich J. C. (1978): The finite element method and convection problems in fluid mechanics. Finite elements in fluids, vol. 3, Gallagher et al. eds., Wiley
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag
About this paper
Cite this paper
Örs, H. (1999). Shallow water model for the bosphorus current. In: Biringen, S., Örs, H., Tezel, A., Ferziger, J.H. (eds) Industrial and Environmental Applications of Direct and Large-Eddy Simulation. Lecture Notes in Physics, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106107
Download citation
DOI: https://doi.org/10.1007/BFb0106107
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66171-9
Online ISBN: 978-3-540-48706-7
eBook Packages: Springer Book Archive