An improved cubic Petrov-Galerkin method for simulation of transient advection-diffusion processes in rectangularly decomposable domains

Efthimios T. Bouloutas, Michael Anthony Celia

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

A modified cubic Petrov-Galerkin method for solution of multidimensional unsteady advection-diffusion problems is proposed. The method is based on a weighted residual formulation in which the trial space is piecewise linear and the test space is a special piecewise cubic space. The test functions are formed by adding a symmetric cubic perturbation to the piecewise linear basis functions. A frequency-fitting algorithm is used to determine the appropriate magnitude of the cubic perturbation. With this frequency fitted parameter, the method is shown to be superior to standard Galerkin and Petrov-Galerkin methods. Both one- and two-dimensional numerical results are presented. The two-dimensional results are for a rotating flow field and demonstrate that the method performs very well in nonconstant velocity fields. The numerical results demonstrate that the accuracy of the cubic Petrov-Galerkin method is comparable to that of a quadratic basis function Galerkin method, with less than half the computational effort.

Original languageEnglish (US)
Pages (from-to)289-308
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Volume92
Issue number3
DOIs
StatePublished - Nov 1991

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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