Linear hybrid unstructured meshes are elevated to high-order meshes using a mesh smoothing scheme. The linear meshes are first elevated to highorder by introducing new edge, face and internal nodes. Then the high-order elements are subdivided into a collection of linear sub-elements. Node perturbation vectors are computed for the new surface nodes. Employing a mesh smoothing/optimization method on the linear sub-elements curves the high-order mesh. The mesh smoothing method is an extension of an optimization-based node perturbation technique that uses a cost function to enforce desired element shapes. Details of the mesh elevation and smoothing process are described. Several three-dimensional examples are included that demonstrate the effectiveness of the method to produce high quality highorder meshes.Nomenclature [A] = Jacobian matrix for condition number C, C min = Cost function, minimum cost function WCN = Weighted condition number J = Magnitude of Jacobian matrix ! p n = Perturbation vector for node n ! s n = Sensitivity vector for node n [W] = Weight matrix for weighted condition number X, Y, Z = Cartesian physical coordinates Ω = Relaxation parameter

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The objective of the Cranked-Arrow Wing Aerodynamics Project International (CAWAPI) was to allow a comprehensive validation of Computational Fluid Dynamics methods against the CAWAP flight database. A major part of this work involved the generation of high-quality computational grids. Prior to the grid generation an IGES file containing the air-tight geometry of the F-16XL aircraft was generated by a cooperation of the CAWAPI partners. Based on this geometry description both structured and unstructured grids have been generated. The baseline structured (multi-block) grid (and a family of derived grids) has been generated by the National Aerospace Laboratory NLR. Although the algorithms used by NLR had become available just before CAWAPI and thus only a limited experience with their application to such a complex configuration had been gained, a grid of good quality was generated well within four weeks. This time compared favourably with that required to produce the unstructured grids in CAWAPI. all-tetrahedral and hybrid unstructured grids has been generated at NASA Langley Research Center and the USAFA, respectively. To provide more geometrical resolution, trimmed unstructured grids have been generated at EADS-MAS, the UTSimCenter, Boeing Phantom Works and KTH/FOI. All grids generated within the framework of CAWAPI will be discussed in the article. Both results obtained on the structured grids and the unstructured grids showed a significant improvement in agreement with flight test data in comparison with those obtained on the structured multi-block grid used during CAWAP. Nomenclature

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A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.