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SUMMARYAfter several years of planning, the 1st International Workshop on High‐Order CFD Methods was successfully held in Nashville, Tennessee, on January 7–8, 2012, just before the 50th Aerospace Sciences Meeting. The American Institute of Aeronautics and Astronautics, the Air Force Office of Scientific Research, and the German Aerospace Center provided much needed support, financial and moral. Over 70 participants from all over the world across the research spectrum of academia, government labs, and private industry attended the workshop. Many exciting results were presented. In this review article, the main motivation and major findings from the workshop are described. Pacing items requiring further effort are presented. Copyright © 2013 John Wiley & Sons, Ltd.

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Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD) include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) methods. The recently proposed Flux Reconstruction (FR) approach or Correction Procedure using Reconstruction (CPR) is based on a differential formulation and provides a unifying framework for these high-order schemes. Here we present a brief review of recent developments for the FR/CPR schemes as well as some pacing items. IntroductionIn the field of Computational Fluid Dynamics (CFD), low -order methods are generally robust and reliable; as a result, they are routinely employed in practical calculations. For the same computing cost, high-order methods can provide considerably more accurate solutions, but they are more complicated and less robust. The need to improve and develop new high-order methods with favorable properties has attracted the interest of many researchers as evidenced by the recently held First (2012) and Second (2013) International Workshops on High-Order CFD Methods.The Discontinuous Galerkin (DG) method is currently among the most widely used high-order numerical methods for solving the compressible Navier-Stokes equations on unstructured meshes. It was introduced for the neutron transport equation by Reed and Hill (1973), analyzed by LaSaint and Raviart (1974) and developed and made popular for fluid dynamics equations by Cockburn,