A Jacobian-free edged-based Galerkin formulation for compressible flows

Song Gao, Wagdi G. Habashi, Dario Isola, Guido S. Baruzzi, Marco Fossati

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8 Citations (Scopus)
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A parallel formulation of a Jacobian-free all Mach numbers solver on unstructured hybrid meshes is proposed. The Finite Element formulation is edge-based with flow stabilization obtained with either AUSM+ -up or Roe scheme. The linear system is solved via a Jacobian-Free Newton-Krylov (JFNK) method with Lower-Upper Symmetric GaussSeidel (LU-SGS) used as matrix-free preconditioner. The traditional formulation of LU-SGS is enriched by including the contributions from viscous fluxes and boundary conditions. The accuracy and efficiency of the proposed approach are demonstrated over cases ranging from low to high Mach numbers: subsonic flow over the Trap Wing, transonic flow over the ONERA M6 wing, supersonic flow over a sphere, supersonic flow over a waverider and finally hypersonic flow over a sphere.
Original languageEnglish
JournalComputers and Fluids
Early online date26 Oct 2016
Publication statusE-pub ahead of print - 26 Oct 2016


  • Jacobian-free
  • unstructured hybrid meshes
  • finite element
  • flow stabilization
  • Newton-Krylov method
  • lower-upper symmetric Gaussian-Seidel
  • viscous fluxes
  • boundary conditions
  • aircraft aerodynamics
  • Mach numbers
  • aero-thermodynamic efficiency
  • Galerkin formulation
  • compressible flows


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