Three-dimensional discontinuous spectral/hp element methods for compressible flows PDF
Preview Three-dimensional discontinuous spectral/hp element methods for compressible flows
Three-dimensional discontinuous spectral/hp element methods for compressible flows by Daniele De Grazia Department of Aeronautics Imperial College London This thesis is submitted for the degree of Doctor of Philosophy of Imperial College London 2016 “Considerate la vostra semenza: fatti non foste a viver come bruti, ma per seguir virtute e canoscenza.” Dante Alighieri, Inferno, Canto XXVI. Declaration This is to certify that the work presented in this thesis has been carried out at Imperial College London and has not been previously submitted to any other uni- versity or technical institution for a degree or award. The thesis comprises only my original work, except where due acknowledgement is made in the text. The copyright of this thesis rests with the author and is made available under a CreativeCommonsAttributionNonCommercialNoDerivativeslicence. Research- ers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. DanieleDeGrazia Acknowledgements I would like to thank all the people who have made this journey towards the PhD a memorable experience. First, I would like to thank my supervisor, Professor Spencer Sherwin, who gavemethisgreatopportunity. ProfessorSherwinintroducedmetothefascinating worldofCFDandpatientlyguidedthroughoutmyresearchpathmakingthisthesis possible. I am also extremely grateful to my co-supervisor Dr Peter Vincent for all the support he provided during my PhD years. The many discussions we had about high-order methods were extremely fruitful and I have really enjoyed collaborating with him. I would also like to express my sincere gratitude to Dr. David Moxey who has never withdrawn his human and technical support during these years. I wish him all the best for his career. I would also like to thank Professor Anatoly Ruban for all the help and assist- ance and Dr Marina Kravtsova for all the fruitful discussions and suggestions. I have greatly enjoyed the company of my colleagues and friends in Mathem- atics: Arshad, Calum Curtis, David, Emma, Hui, Jamie, Joe, Liam, Mat, Max- imilian, Nikos, Radu, Raquel, Ruben, Thomas and Tomass as well as the time spent with my colleagues and friends in Aeronautics: Alessandro, Bastien, Chris, Dirk, Douglas, Gabriele, Justin, Laurent, Lisa, Olya, Rodrigo, Thibault. A special thanks goes to my friend Gianmarco who was the first to convince me to undertake this PhD challenge which has been a great experience and with whom I shared a lot of unforgettable moments. I will always remember the good times we had in the lab and in London. I am also extremely grateful to my friends Jean and Mario who helped me to keep my sanity during these research years and made the PhD more enjoyable. IwouldalsoliketothankallthefriendsandrelativesinItalywhichhavealways made me feel close to home during these years. I am extremely grateful to my parents and my brother for their continuous support. All of this would have never been possible without all their love and support. Above all, I thank Fabiana. She always encouraged me to pursue my passions and has always been supportive during these years convincing me to not give up, so I would like to dedicate this thesis to her. Abstract In this thesis we analyse and develop two high-order schemes which belong to the class of discontinuous spectral/hp element methods focusing on compressible aerodynamic studies and, more specifically, on boundary-layer flows. We invest- igate the discontinuous Galerkin method and the flux reconstruction approach providing a detailed analysis of the connections between these methods. The con- nections found enable a better understanding of the broader class of discontinuous spectral/hp element methods. From this perspective it was evident that some of the issues of the discontinu- ousGalerkinmethodarealsoencounteredinthefluxreconstructionapproach, and in particular, the aliasing errors of the two schemes are identical. The techniques applied in the more famous discontinuous Galerkin method for tackling these er- rors can be also extended to the flux reconstruction approach. We present two dealiasing strategies based on the concept of consistent integration of the nonlin- ear terms. The first is a localised approach which targets in each element the nonlinearities arising in the problem, while the second is a more global approach which involves a higher quadrature of the overall right-hand side of the discretised equation(s). Both the strategies have been observed to be effective in enhancing the robustness of the schemes considered. We finally present the direct numerical simulation of a high-speed subsonic boundary-layerflowpastathree-dimensionalroughnesselement,achievedbymeans ofthecompressibleaerodynamicsolverdeveloped. Thistypeofanalyseshavebeen widely performed in the past with approximated theories. Only recently, has DNS been used due to the improvement of numerical techniques and an increase in computational resources for similar studies in low-speed subsonic, supersonic and hypersonic regimes. This thesis takes a first step to close the gap between the res- ults for a high-speed subsonic regime and the results in supersonic and hypersonic regimes. i ii
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