Multigrid solution of compressible turbulent flow on unstructured meshes using a two‐equation model

D. J. Mavriplis, Luigi Martinelli

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33 Scopus citations


The steady state solution of the system of equations consisting of the full Navier‐Stokes equations and two turbulence equations has been obtained using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge‐Kutta time‐stepping scheme with a stability‐bound local time step, while the turbulence equations are advanced in a point‐implicit scheme with a time step which guarantees stability and positivity. Low‐Reynolds‐number modifications to the original two‐equation model are incorporated in a manner which results in well‐behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved, initializing all quantities with uniform freestream values. Rapid and uniform convergence rates for the flow and turbulence equations are observed.

Original languageEnglish (US)
Pages (from-to)887-914
Number of pages28
JournalInternational Journal for Numerical Methods in Fluids
Issue number10
StatePublished - May 30 1994

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


  • Meshes
  • Multigrid
  • Turbulence
  • Unstructured


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