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High-Order Accurate Implicit Method Rotor

This study demonstrates the feasibility of utilizing an innovative high-order accurate implicit method to obtain high-resolution numerical solutions of the compressible Navier-Stokes equations required in problems of interest to rotorcraft applications. The ultimate goal of the overall effort is to develop a complete software package to be used by engineers for analysis and design of modern helicopter rotors. The method uses high-order compact, central-difference operators for the discretization of spatial derivatives of both the explicit right-hand-side terms and the implicit operators. The essential features of the method have been implemented into the data-structure of the rotary-wing version of the OVERFLOW code. Currently fourth order of accuracy can be achieved on regular, single block meshes and problems with smooth solutions, where the farfield boundary conditions have little effect on the overall accuracy level, and they can be approximated by one-dimensional Riemann invariant extrapolation. Applications are presented for a simple vortex convection by a uniform freestream and for a two-dimensional blade vortex interaction problem. This preliminary implementation of the proposed method provides a successful demonstration of the approach and has potential applications for NASA and commercial aerospace companies.

The present low-cost, high-order accurate prediction method can be used to improve rotor blade design and as advanced analysis tool for investigation of rotor aerodynamics. This method contributes to efforts for improving helicopter and fixed wing aircraft performance and noise emission characteristics while reducing analysis and design cycle time.


  1. Ekaterinaris, J. A., "Application of High-Order Accurate Implicit Method to Rotor Aerodynamics," NEAR TR 556, Nielsen Engineering & Research, Mountain View, CA, June 2000.
  2. Ekarinaris, J. A., "Implicit High-Order Methods for Gasdynamics and Aeroacoustics," Journal of Computational Physics, Vol. 156, No. 2, 1999, pp. 272-299.
  3. Ekarinaris, J. A., "Implicit High-Order Accurate in Space Algorithms for the Navier-Stokes Equations," AIAA Journal, Vol. 38, No. 6, Jun. 2000.

MDO Design Aeroelasticity
MDO Design Configuration
Unstructured MacroCell Methodology for Dynamic Stall
High-Order Accurate Implicit Method to Rotor Aerodynamics
Turbulent Flow Aero-Optical Distortion



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