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Diffusion Problem

  • Lars Petter RøedEmail author
Chapter
  • 685 Downloads
Part of the Springer Textbooks in Earth Sciences, Geography and Environment book series (STEGE)

Abstract

In this chapter, we discuss the fundamentals of how to cast a PDE into finite difference form. More specifically, the reader will learn how to discretize the diffusion equation, and learn why some discretizations work and some do not. This will be the opportunity to introduce concepts such as numerical stability, convergence, and consistency. It will be explained how to check whether a discretization is stable and consistent, and the reader will learn about explicit and implicit schemes, the rudiments of elliptic solvers, and the concept of numerical dissipation or artificial damping inherent in our discretizations.

Keywords

Elliptic Solver Numerical Dissipation Implicit Scheme Finite Difference Version Crank-Nicholson Scheme 
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

  1. Abramowitz M, Stegun I (1965) Handbook of mathematical functions, 9th edn. Dover Publications, Inc, New YorkGoogle Scholar
  2. Adamec D, O’Brien JJ (1978) The seasonal upwelling in the Gulf of Guinea due to remote forcing. J Phys Oceanogr 8:1050–1060CrossRefGoogle Scholar
  3. Gill AE (1982) Atmosphere–ocean dynamics. International geophysical series, vol 30. Academic, New YorkGoogle Scholar
  4. Griffies SM (2004) Fundamentals of ocean climate models. Princeton University Press, Princeton. ISBN 0-691-11892-2Google Scholar
  5. Lax PD, Richtmyer RD (1956) Survey of the stability of linear finite difference equations. Commun Pure Appl Math 9:267–293, MR 79,204.  https://doi.org/10.1002/cpa.3160090206
  6. Phillips OM (1966) The dynamics of the upper ocean. Cambridge University Press, New York, 269 ppGoogle Scholar
  7. Yoshida K (1959) A theory of the Cromwell current and of equatorial upwelling. J Oceanogr Soc Jpn 15:154–170CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of GeosciencesUniversity of OsloOsloNorway
  2. 2.Norwegian Meteorological InstituteOsloNorway

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