A stable high-order finite difference scheme for the compressible Navier-Stokes equations. No-slip wall boundary conditions

Magnus Svärd, Jan Nordström

Research output: Contribution to journalArticlepeer-review

165 Citations (Scopus)

Abstract

A stable wall boundary procedure is derived for the discretized compressible Navier-Stokes equations. The procedure leads to an energy estimate for the linearized equations. We discretize the equations using high-order accurate finite difference summation-by-parts (SBP) operators. The boundary conditions are imposed weakly with penalty terms. We prove linear stability for the scheme including the wall boundary conditions. The penalty imposition of the boundary conditions is tested for the flow around a circular cylinder at Ma = 0.1 and Re = 100. We demonstrate the robustness of the SBP-SAT technique by imposing incompatible initial data and show the behavior of the boundary condition implementation. Using the errors at the wall we show that higher convergence rates are obtained for the high-order schemes. We compute the vortex shedding from a circular cylinder and obtain good agreement with previously published (computational and experimental) results for lift, drag and the Strouhal number. We use our results to compare the computational time for a given for a accuracy and show the superior efficiency of the 5th-order scheme.

Original languageEnglish
Pages (from-to)4805-4824
Number of pages20
JournalJournal of Computational Physics
Volume227
Issue number10
DOIs
Publication statusPublished - 1 May 2008
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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