Download or read book Mesh and Polynomial Adaptation for High-order Discretizations of Compressible Flows written by Jean-Sébastien Cagnone and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The aerospace research and industry sectors are relying increasingly on numerical simulations to gain insight into aerodynamic flows. However, the complexity of these flows and the broad range of scales they exhibit still represent a serious challenge to the current generation of computational methods. This thesis presents developments to high-order accurate (> 2nd order) schemes aimed at addressing these limitations. The topic is tackled from the perspectives of enhanced resolution and adaptive error-control. Firstly, an extension of the Lifting-Collocation-Penalty (LCP) scheme to spatially-varying polynomial approximations is presented. This formulation is used to perform efficient polynomial-adaptive computations of compressible flows. The focus is put on the adequate inter-cell flux transfer, and stability analysis of the resulting scheme. Secondly, improved error-control via adjoint-driven mesh refinement is demonstrated. The connection between the global error-norm and the truncation error is established through an adjoint problem. This link provides valuable information about error-propagation patterns, and is shown to be useful for adaptive mesh refinement. " --