A mixed Fourier-Galerkin-finite-volume method to solve the fluid dynamics equations in cylindrical geometries

Jóse Núñez, Eduardo Ramos, Juan Lopez

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the FourierGalerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems.

Original languageEnglish (US)
Article number031414
JournalFluid Dynamics Research
Volume44
Issue number3
DOIs
StatePublished - Jun 2012

ASJC Scopus subject areas

  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes

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