American Institute of Aeronautics and Astronautics 092407 1 Strategies for Driving Mesh Adaptation in CFD (Invited) Christopher J. Roy 1 Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061 This paper examines different approaches for driving mesh adaptation and provides theoretical developments for understanding the relationship between discretization error, the numerical scheme, and the mesh. Discrete and continuous equations governing the transport of discretization error are developed and it is shown that the truncation error acts as the local source for these equations. Examination of the truncation error in generalized coordinates provides insight into the role of mesh quality (mesh stretching for the 1D case) in the discretization error. Numerical results are presented for 1D steady-state Burgers equation at Reynolds numbers of 32 and 128. Four different approaches for driving mesh adaption are implemented for this case: solution gradients, solution curvature, discretization error, and truncation error. The truncation-error based adaption is shown to provide superior results for both cases. Finally, two approaches for estimating the truncation error are also discussed which would allow truncation error-based adaption to be implemented for complex numerical methods. I. Introduction ISCRETIZATION error occurs in every Computational Fluid Dynamics (CFD) solution and is often one of the main contributors to the overall uncertainty in a CFD prediction. It is formally defined as the difference between the exact solution to the discrete equations and the exact solution to the governing partial differential equations. Discretization error is the most difficult type of numerical error to estimate and is usually the largest of the numerical error sources, which also include iterative error, round-off error, and statistical error (where relevant). There are a number of different approaches for estimating discretization error, but they all rely on the underlying numerical solution (or solutions) being in the asymptotic range with regards to either the truncation error or the discretization error. In addition to the importance of estimating the discretization error, we also desire methods for reducing it. Applying uniform mesh refinement (required for extrapolation-based discretization error estimation such as Richardson extrapolation) is not the most efficient method for reducing the discretization error. Since uniform refinement, by definition, uniformly refines over the entire domain, it generally results in meshes with highly- refined cells/elements in regions where they are not needed. For 3D CFD applications, each time the mesh is refined by grid doubling in each coordinate direction, the number of cells/elements increases by a factor of eight. Thus uniform refinement for reducing discretization error can be extremely expensive. Targeted local refinement, or mesh adaptation, is a much better strategy for reducing the discretization error. There have been several extensive reviews of mesh adaption approaches for CFD (e.g., see Baker 1 and McRae 2 ); however much of this work has focused on methods for actually performing the adaption rather than the approach for driving the mesh adaptation. This paper examines several different criteria for driving a mesh adaptation scheme. After a brief discussion of different methods for determining which regions should be refined and which regions should be coarsened, the simple approach to mesh adaption is described. Then an extensive discussion of the truncation error and its relationship to the discretization error is given. Results are then given for the different mesh adaption methods applied to 1D steady-state Burgers equation for a viscous shock wave, followed by a discussion of two methods for approximating the truncation error. 1 Associate Professor, Aerospace and Ocean Engineering Department, 215 Randolph Hall, Associate Fellow AIAA. D 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5 - 8 January 2009, Orlando, Florida AIAA 2009-1302 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.