Adjoint-Based Hp-Adaptation for a Class of High-Order Hybridized Finite Element Schemes for Compressible Flows

Balan, Aravind; Woopen, Michael; May, Georg

doi:10.2514/6.2013-2938

Cited by 10 publications

(21 citation statements)

References 13 publications

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“…The work also involved trying out various smoothness sensors, available in literature [80,69,65], to choose between h-or p-refinement, and obtaining the most robust sensor. Results using one such sensor, based on the decay of expansion coefficients, were presented in an AIAA conference [8]. In the present work, a more robust sensor which is based on a measure of the inter-element jumps in the solution [29] is employed to obtain the presented results.…”

Section: Extending the Hdg Code To Handle Hp-adaptivity On Isotropic mentioning

confidence: 99%

“…This can be exploited to create a local smoothness sensor. Although it works very well, we have found that we cannot use a unique criteria to choose between h− and p-refinement for different test cases [8]. This means, for different test cases, we need to find the best criteria using trial and error method, which is a severe drawback.…”

Section: Adjoint-based Hp-adaptationmentioning

confidence: 99%

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Adjoint-based hp -adaptivity on anisotropic meshes for high-order compressible flow simulations

2016

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reibungsfreien subsonischen, transsonischen und supersonischen und viskosen subsonischen Strömungen um ein NACA0012 Profil. First and foremost, I would like to thank my advisor Prof. Georg May for his supervision, kindness and encouragement throughout my time at AICES Graduate School. I consider my association with Georg as one of the most rewarding and formative experiences in my career. Apart from imparting his knowledge in numerical methods, Georg has always shown considerable patience while guiding me through various phases of my research. I am sure his students will continue to be inspired by his work ethic, knowledge, the rigour with which he pursues his research, and his sheer professionalism. I would like to thank Prof. Siegfried Müller for being part of my doctoral committee. I really appreciate his painstaking review of my thesis. His insightful feedback was indispensable in having the thesis in its current refined form. I am also grateful to Prof. Herbert Olivier for taking the time and effort to chair the doctoral committee. Many thanks are due to my colleague Michael Woopen with whom I did much of my doctoral research. Michael would always come to my aid whenever I had any issue with the code or any technical or theoretical query that needed clarification. His support was nothing short of significant during the course of my research. I would also like to thank my colleagues Francesca and Jochen who were promptly obliging whenever I sought their help. I am also grateful to Ajay for our many stimulating, mutually beneficial discussions. I consider it an honor to be a part of the research at AICES graduate school, and I appreciate all those who were part of my life here. A debt of gratitude is owed to the AICES service team led by Dr. Nicole Faber who did a wonderful job in supporting all of us. Nicole's administrative and organisational abilities deserve a special mention. Finally, I would like to express my sincere thanks to my family and friends for being there for me always.

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Section: Extending the Hdg Code To Handle Hp-adaptivity On Isotropic mentioning

confidence: 99%

Section: Adjoint-based Hp-adaptationmentioning

confidence: 99%

Adjoint-based hp -adaptivity on anisotropic meshes for high-order compressible flow simulations

2016

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“…Adaptation in the temporal domain alone is obviously not enough to get the full potential of a method. Spatial adaptation is already available in the solver [44], and temporal adaptation has been investigated in this paper. Future work should therefore couple both ingredients in a sophisticated way to achieve maximum efficiency.…”

Section: Discussionmentioning

confidence: 99%

A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows

Jaust

Schütz

2014

Computers & Fluids

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The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can, e.g., be done by backward difference formulae (BDF) or diagonally implicit Runge-Kutta (DIRK) methods. In this work, we investigate the use of embedded DIRK methods in an HDG solver, including the use of adaptive time-step control. Numerical results demonstrate the performance of the method for both linear and nonlinear (systems of) time-dependent convection-diffusion equations.

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“…2 Note the amplification factor N 1 in the y-axis is a logarithmic quantity. 3 Note the amplitude of the instabilities in Figure 3 is non-dimensionalized with respect to the freestream velocity.…”

Section: Transitional Flow Over the Naca 65-(18)10 Compressor Cascadementioning

confidence: 99%

Hybridized Discontinuous Galerkin Methods for Wave Propagation

et al. 2018

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We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (i) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (ii) a judicious choice of the numerical flux to provide stability and consistency; and (iii) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems. *

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Adjoint-Based Hp-Adaptation for a Class of High-Order Hybridized Finite Element Schemes for Compressible Flows

Cited by 10 publications

References 13 publications

Adjoint-based hp -adaptivity on anisotropic meshes for high-order compressible flow simulations

Adjoint-based hp -adaptivity on anisotropic meshes for high-order compressible flow simulations

A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows

Hybridized Discontinuous Galerkin Methods for Wave Propagation

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