Summary
A 2D algorithm for free surface flow and salinity transport in coastal areas on a ‘multiple instruction multiple data’ (MIMD) parallel computer with 128 processors is presented. Operator splitting in the basic equations leads to a separated treatment of the hyperbolic and parabolic terms, which are then combined by coupling the Method of Characteristics with the Finite Element technique. Different iterative solvers based on conjugate gradient methods and different preconditioners are used for solving the two sets of linear equations. The data of the unstructured grids are distributed among the processors with Recursive Spectral Bisection in combination with the Kernighan-Lin heuristic. The performance of the implemented algorithm is demonstrated using a field case study of the German estuary ‘Darß-Zingster Boddenkette’.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barret, R. et al.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, email: templates@cs.utk.edu, 1993.
Bastian, P.: Parallele adaptive Mehrgitterverfahren, Thesis, Institut für Computeranwendungen, Universität Stuttgart, 1994.
Hackbusch, W.: Iterative Lösung großer schwachbesetzter Gleichungssysteme, B. G. Teubner, Stuttgart, 1991.
Hendrickson, B. and Leland, R.: The Chaco User’s Guide Version 1.0, Sandia National Laboratories, Albuquerque, USA, 1993.
Hughes, J.R., Ferencz, M. and Hallquist, O.: Large Scale Vectorized Implicit Calculations in Solid Mechanics on a CrayX-MP/48 Utilizing EBE Preconditioned Conjugate Gradients, Computer Methods in Applied Mechanics and Engineering 61, North-Holland, 1987.
Lepeintre, F.: Bibliotheque BIEF — Note de Principe et Descriptif Informatique, EDF report HE-43/92-16, Chatou, France, 1992.
Farhat, C., Lanteri, S. and Simon, H.D.: TOP/DOMDEC — A Software Tool for Mesh Partitioning and Parallel Processing, Department of Aerospace Sciences and Center for Space Structures and Controls, University of Colorado and NASA Ames Research Center, Moffett Field, Colorado, USA, 1994.
Galland, J.C., Goutal, N. and Hervouet, J.M.: Telemac: A New Numerical Model for Solving Shallow Water Equations, Advanced Water Resources, Vol. 14, No. 3, 1991.
Kernighan, B.W. and Lin, S.: An Efficient Heuristic Procedure for Partitioning Graphs, The Bell System, Technical Journal 49, 1970.
Simon, H.D.: Partitioning of Unstructured Problems for Parallel Processing, NASA Ames Research Center, Moffett Field, Colorado, USA, 1994.
Stückrad, H., Hinkelmann, R. and Zielke, W.: Hydrodynamisch-numerische Modellierung der Darß-Zingster Boddenkette, Deutsche Hydrographische Zeitschrift, Heft 2, 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Hinkelmann, R., Zielke, W. (1997). A Parallel 2D Operator Splitting Method for the Navier-Stokes and Transport Equations. In: Helmig, R., Jäger, W., Kinzelbach, W., Knabner, P., Wittum, G. (eds) Modeling and Computation in Environmental Sciences. Notes on Numerical Fluid Mechanics (NNFM), vol 59. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89565-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-322-89565-3_18
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-89567-7
Online ISBN: 978-3-322-89565-3
eBook Packages: Springer Book Archive