Numerical analysis of time accuracy of a primitive variable-based formulation of the conservative form of the governing equations for compressible flows

Huaibao Zhang, Alexandre Martin, Guangxue Wang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A class of Computational Fluid Dynamics codes uses primitive variable-based formulation to solve the conservative form of the governing equations. Under certain specific conditions, the approach yields inaccurate results for unsteady problems. Here, Euler equations are used to numerically analyse time accuracy when using such an approach. It is demonstrated, using a simple shock tube problem, that the primitive variable-based approach does not strictly preserve time accuracy. A dual-time stepping technique, which uses an inner iteration of pseudo-time within the physical time, is used to correct the issue. The method is applied to the shock tube problem, which eliminates the time-dependent discrepancies. The problem, and the correction, is also applied to a supersonic flow over a wedge. In both cases, the results are shown to be identical to the solution obtained using a conservative variable-based approach.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalInternational Journal of Computational Fluid Dynamics
Volume33
Issue number1-2
DOIs
StatePublished - Feb 7 2019

Bibliographical note

Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • Conservative property
  • compressible flow
  • dual-time stepping
  • primitive variables
  • time accuracy

ASJC Scopus subject areas

  • Computational Mechanics
  • Aerospace Engineering
  • Condensed Matter Physics
  • Energy Engineering and Power Technology
  • Mechanics of Materials
  • Mechanical Engineering

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