Very Efficient Third-Order CFD Solver

Very Efficient Third-Order CFD Solver


Develop a third-order method for 3D unstructured grids:

  • Very low-cost 3rd-order method
  • High-order curved grids not required
  • Accurate vorticity (gradient) prediction
  • Improved convergence


  • Development of high-order methods presents a major challenge in large-scale turbulent-flow simulations over realistic complex geometries
  • Efficient discretizations and solvers and high-order grid generation remain major pacing items
  • Accurate gradients are critical to reliable turbulent simulations, but current methods for unstructured grids are lower-order and prone to numerical noise


3rd-order edge-based method:

  • Quadratic LSQ, flux extrapolation, and source
    quadrature make a current CFD code to high-order

Hyperbolic Navier-Stokes method:

  • Reformulate the viscous term as a hyperbolic system with gradients as additional unknowns


  • Implemented in NASA’s FUN3D, and accurate gradients demonstrated (AIAA2016-3969)
  • Unsteady extension presented at SciTech2017
  • Being extended to fully third-order accurate Turbulent flow simulations

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