SUMMARY We examine the numerical solution of the adjoint quasi‐one‐dimensional Euler equations with a central‐difference finite volume scheme with Jameson‐Schmidt‐Turkel (JST) dissipation, for both the continuous and discrete approaches. First, the complete formulations and discretization of the quasi‐one‐dimensional Euler equations and the continuous adjoint equation and its counterpart, the discrete adjoint equation, are reviewed. The differences between the continuous and discrete boundary conditions are also explored. Second, numerical testing is carried out on a symmetric converging–diverging duct under subsonic flow conditions. This analysis reveals that the discrete adjoint scheme, while being manifestly less accurate than the continuous approach, gives nevertheless more accurate flow sensitivities. Copyright © 2011 John Wiley & Sons, Ltd.

Mesh adaptation based on error estimation has become a key technique to improve the accuracy of computationalfluid-dynamics computations. The adjoint-based approach for error estimation is one of the most promising techniques for computational-fluid-dynamics applications. Nevertheless, the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method. In the present investigation, a new mesh refinement method based on estimation of truncation error is presented in the context of finite-volume discretization. The T estimation method uses auxiliary coarser meshes to estimate the local truncation error, which can be used for driving an adaptation algorithm. The method is demonstrated in the context of two-dimensional NACA0012 and three-dimensional ONERA M6 wing inviscid flows, and the results are compared against the adjoint-based approach and physical sensors based on features of the flow field.

The necessity to modify a pre-existing computational mesh is a common requirement in many areas of computational fluid dynamics like aeroelasticity, optimization, etc. Here, we propose an approach to develop an efficient numerical mesh movement tool. The strategy relies on a three steps procedure: (i) generation of an octree decomposition of the geometry, (ii) definition of small interpolation domains, and (iii) application of local interpolation algorithms. Deformation is propagated from the moving boundaries towards the far field in a way similar to an advancing front methodology, which ensures continuity and numerical viability. The method can be applied to any type of mesh: structured, multiblock structured, unstructured and hybrid because it only uses geometric position of the mesh points, regardless of the particular mesh connectivities. The interpolation tool is based on radial basis functions. It will be showed that the method is very robust and generates a mesh with similar quality parameters as the original, it is computationally very efficient and can be easily parallelized.

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