A Multiscale Pressure Splitting of the Shallow-Water Equations: I. Formulation and 1D Tests

Olivier Le Maître*, Julia Levin, Mohamed Iskandarani, Omar M. Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Direct representation of the free surface in ocean circulation models leads to a number of computational difficulties that are due to the fast time scales associated with free-surface waves. These fast time scales generally result in severe time-step restrictions when the free surface is advanced using an explicit scheme and may result in large phase errors when the free surface is treated implicitly with a large time step. A multiple-scale analysis of the shallow-water equations is used to analyze this stiffness and to guide the construction of a computational methodology that overcomes the associated difficulties. Specifically, we explore a class of fractional step methods that utilize coarsened grids in the propagation of long-wave data. The behavior of the corresponding schemes is examined in detail in light of one-dimensional model problems, based on finite-difference or spectral-element discretizations.

Original languageEnglish (US)
Pages (from-to)116-151
Number of pages36
JournalJournal of Computational Physics
Issue number1
StatePublished - Jan 1 2001
Externally publishedYes


  • Aymptotic analysis
  • Filtering
  • Ocean circulation
  • Operator splitting
  • Spectral elements

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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