Symbolic Computation as a Tool for High-Order Long-Wave Stability Analysis of Thin Film Flows with Coupled Transport Processes

U. Lange*, K. Nandakumar, H. Raszillier

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Many fundamental studies based on the evolution equations derived by long-wave approximation have contributed to the fact that the dynamics of a thin film flowing down an inclined plane is now one of the best-understood problems of hydrodynamic stability. In most engineering applications however, the stability behaviour of the film flow is modified by complex coupled transport processes, and because of the huge amount of algebra needed to derive the evolution equations in these cases, an investigation by numerical methods is often preferred by engineers. In this paper, we illustrate how computer algebra techniqes can be used to derive and analyse long-wave evolution equations even for very complex situations automatically, thus making the advantages of symbolic solutions available for such applications. Using these methods, higher-order approximations can also be obtained automatically. These are of interest since they can provide heuristic estimates for - and extensions of - the range of validity of the long-wave approximation.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Computational Physics
Volume150
Issue number1
DOIs
StatePublished - 20 Mar 1999
Externally publishedYes

Keywords

  • Automated algorithms
  • Hydrodynamic stability
  • Nonlinear effects
  • Numerical analysis

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