A two-dimensional linearized unsteady Euler scheme for pulse response calculations

A. L. Gaitonde, D. P. Jones*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)


An unsteady linearized Euler scheme for use on moving meshes is presented. This is derived from a scheme for the full non-linear unsteady Euler equations. This scheme is based on the Jameson cell-centred scheme, but is time-accurate and includes the necessary terms to account for grid motion. It is assumed that the unsteadiness in the flow and mesh is small. Using this assumption the discrete unsteady Euler equations are linearized about the full, non-linear, steady mean flow. The resulting equations are solved in the work presented here using a dual-time scheme. In the basic scheme no assumptions are made about the form of the perturbations other than that they are small. This permits the direct calculation of non-periodic flows, e.g. pulse responses. Linear pulse responses are a useful tool as they can be used to calculate the flow due to general inputs. The equations that would result from the assumption of harmonic flow are also derived. Results are presented for heave, pitch and ramp test cases and compared to full non-linear Euler results calculated using a dual-time scheme.

Translated title of the contributionA two-dimensional linearized unsteady Euler scheme for pulse response calculations
Original languageEnglish
Pages (from-to)89-104
Number of pages16
JournalProceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering
Issue number2
Publication statusPublished - 14 Sep 2002

Bibliographical note

Publisher: Institution of Mechanical Engineering


  • Dual-time scheme
  • Linear pulse responses
  • Linearized unsteady Euler scheme
  • Moving meshes

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