subject:(Adjoint based Adaptation)

1. Gauci, Éléonore. Adaptation de maillage orientée fonctionnelle et basée sur une métrique pour des simulations aérodynamiques en géométrie variable : Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries.

Degree: Docteur es, Sciences pour l'ingénieur, 2018, Université Côte d'Azur (ComUE)

URL: http://www.theses.fr/2018AZUR4227

En ce qui concerne les problèmes de Dynamique des Fluides Numériques, l’adaptation du maillage est intéressante pour sa capacité à aborder la convergence asymptotique et à obtenir une prévision précise pour des flux complexes à moindre coût. La méthode d’adaptation de maillage anisotrope réduit le nombre de degrés de liberté nécessaires pour atteindre la précision d’une solution donnée, ce qui a un impact positif sur le temps de calcul. De plus, il réduit la dissipation du schéma numérique en tenant compte automatiquement de l'anisotropie des phénomènes physiques à l'intérieur du maillage. Deux approches principales existent dans la littérature. L'adaptation du maillage basée sur les caractéristiques géométriques, qui est principalement déduite d'une estimation de l'erreur d'interpolation utilisant la hessienne du senseur choisi, contrôle l'erreur d'interpolation du capteur sur l'ensemble du domaine de calcul. Une telle approche est facile à mettre en place et a un large éventail d’applications, mais elle ne prend pas en compte l’EDP considérée utilisée pour résoudre le problème. D'autre part, l'adaptation de maillage orientée fonctionnelle, qui se concentre sur une fonctionnelle scalaire, prend en compte à la fois la solution et l'EDP dans l'estimation d'erreur grâce à l'état adjoint. Mais, la conception de cette estimation d'erreur est beaucoup plus compliquée. Cette thèse présente les résultats obtenus avec différentes méthodes de Dynamique des Fluides Numériques: les solveurs de flux arbitrairement lagrangiens-eulériens (ALE) avec schémas explicites et implicites sont présentés et couplés au mouvement de maillage, l’adaptation de maillage feature-based instationnaire pour les géométries mobiles prend en compte les changements des connectivités de maillage durant toute la simulation, l'état adjoint est étendu aux problèmes de géométries mobiles et l'adaptation de maillage instationnaire orientée fonctionnelle pour les maillages mobiles est déduite d'une estimation d'erreur a priori. Plusieurs exemples numériques issus du secteur aéronautique et du domaine de sécurité civile sont considérés.

When dealing with CFD problems, mesh adaptation is interesting for its ability to approach the asymptotic convergence and to obtain an accurate prediction for complex flows at a lower cost. Anisotropic mesh adaptation method reduces the number of degrees of freedom required to reach a given solution accuracy, thus impact favorably the CPU time. Moreover, it reduces the numerical scheme dissipation by automatically taking into account the anisotropy of the physical phenomena inside the mesh. Two main approaches exist in the literature. Feature-based mesh adaptation which is mainly deduced from an interpolation error estimate using the Hessian of the chosen sensor controls the interpolation error of the sensor over the whole computational domain. Such approach is easy to set-up and has a wide range of application, but it does not take into account the considered PDE used to solve the problem. On the other hand, goal-oriented…

Advisors/Committee Members: Alauzet, Frédéric (thesis director), Dervieux, Alain (thesis director).

Subjects/Keywords: Adaptation de maillage basée métrique; Anisotropie; Adjoint; Simulations instationnaires; Mouvement de maillage; ALE; Metric-based mesh adaptation; Anisotropy; Adjoint; Unsteady simulations; Moving mesh; ALE

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APA (6^th Edition):

Gauci, E. (2018). Adaptation de maillage orientée fonctionnelle et basée sur une métrique pour des simulations aérodynamiques en géométrie variable : Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries. (Doctoral Dissertation). Université Côte d'Azur (ComUE). Retrieved from http://www.theses.fr/2018AZUR4227

Chicago Manual of Style (16^th Edition):

Gauci, Éléonore. “Adaptation de maillage orientée fonctionnelle et basée sur une métrique pour des simulations aérodynamiques en géométrie variable : Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries.” 2018. Doctoral Dissertation, Université Côte d'Azur (ComUE). Accessed April 16, 2021. http://www.theses.fr/2018AZUR4227.

MLA Handbook (7^th Edition):

Gauci, Éléonore. “Adaptation de maillage orientée fonctionnelle et basée sur une métrique pour des simulations aérodynamiques en géométrie variable : Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries.” 2018. Web. 16 Apr 2021.

Vancouver:

Gauci E. Adaptation de maillage orientée fonctionnelle et basée sur une métrique pour des simulations aérodynamiques en géométrie variable : Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries. [Internet] [Doctoral dissertation]. Université Côte d'Azur (ComUE); 2018. [cited 2021 Apr 16]. Available from: http://www.theses.fr/2018AZUR4227.

Council of Science Editors:

Gauci E. Adaptation de maillage orientée fonctionnelle et basée sur une métrique pour des simulations aérodynamiques en géométrie variable : Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries. [Doctoral Dissertation]. Université Côte d'Azur (ComUE); 2018. Available from: http://www.theses.fr/2018AZUR4227

2. Dahm, Johann. Toward Accurate, Efficient, and Robust Hybridized Discontinuous Galerkin Methods.

Degree: PhD, Aerospace Engineering, 2017, University of Michigan

URL: http://hdl.handle.net/2027.42/137150

Computational science, including computational fluid dynamics (CFD), has become an indispensible tool for scientific discovery and engineering design, yet a key remaining challenge is to simultaneously ensure accuracy, efficiency, and robustness of the calculations. This research focuses on advancing a class of high-order finite element methods and develops a set of algorithms to increase the accuracy, efficiency, and robustness of calculations involving convection and diffusion, with application to the inviscid Euler and viscous Navier-Stokes equations. In particular, it addresses high-order discontinuous Galerkin (DG) methods, especially hybridized (HDG) methods, and develops adjoint-based methods for simultaneous mesh and order adaptation to reduce the error in a scalar functional of the approximate solution to the discretized equations. Contributions are made in key aspects of these methods applied to general systems of equations, addressing the scalability and memory requirements, accuracy of HDG methods, and efficiency and robustness with new adaptation methods. First, this work generalizes existing HDG methods to systems of equations, and in so doing creates a new primal formulation by applying DG stabilization methods as the viscous stabilization for HDG. The primal formulation is shown to be even more computationally efficient than the existing methods. Second, by instead keeping existing viscous stabilization methods and developing a new convection stabilization, this work shows that additional accuracy can be obtained, even in the case of purely convective systems. Both HDG methods are compared to DG in the same computational framework and are shown to be more efficient. Finally, the set of adaptation frameworks is developed for combined mesh and order refinement suitable for both DG and HDG discretizations. The first of these frameworks uses hanging-node-based mesh adaptation and develops a novel local approach for evaluating the refinement options. The second framework intended for simplex meshes extends the mesh optimization via error sampling and synthesis (MOESS) method to incorporate order adaptation. Collectively, the results from this research address a number of key issues that currently are at the forefront of high-order CFD methods, and particularly to output-based hp-adaptation for DG and HDG methods. Advisors/Committee Members: Fidkowski, Krzysztof J (committee member), Krasny, Robert (committee member), May, Georg (committee member), Powell, Ken (committee member).

Subjects/Keywords: Computational Fluid Dynamics; High-Order Methods; Discontinous Galerkin Methods; Adjoint-Based Error Estimation; Mesh and Order Adaptation; Aerospace Engineering; Engineering

…example mesh (left) obtained by anisotropic adaptation using metric-based global re… …hybridized (HDG) methods, and develops adjoint-based methods for simultaneous mesh and… …these xii frameworks uses hanging-node-based mesh adaptation and develops a novel local… …specifically the adjoint-based algorithms for determining how both the error estimate and the… …adjoint field based on the specified output functional, the error estimation can provide a local…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Dahm, J. (2017). Toward Accurate, Efficient, and Robust Hybridized Discontinuous Galerkin Methods. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/137150

Chicago Manual of Style (16^th Edition):

Dahm, Johann. “Toward Accurate, Efficient, and Robust Hybridized Discontinuous Galerkin Methods.” 2017. Doctoral Dissertation, University of Michigan. Accessed April 16, 2021. http://hdl.handle.net/2027.42/137150.

MLA Handbook (7^th Edition):

Dahm, Johann. “Toward Accurate, Efficient, and Robust Hybridized Discontinuous Galerkin Methods.” 2017. Web. 16 Apr 2021.

Vancouver:

Dahm J. Toward Accurate, Efficient, and Robust Hybridized Discontinuous Galerkin Methods. [Internet] [Doctoral dissertation]. University of Michigan; 2017. [cited 2021 Apr 16]. Available from: http://hdl.handle.net/2027.42/137150.

Council of Science Editors:

Dahm J. Toward Accurate, Efficient, and Robust Hybridized Discontinuous Galerkin Methods. [Doctoral Dissertation]. University of Michigan; 2017. Available from: http://hdl.handle.net/2027.42/137150

University of Kansas

3. Shi, Lei. Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.

Degree: PhD, Aerospace Engineering, 2014, University of Kansas

URL: http://hdl.handle.net/1808/27533

High-order methods have the potential to achieve higher accuracy at lower cost than lower order methods. This potential has been demonstrated conclusively for smooth problems in the 1st International Workshop on High-Order Methods. For non-smooth problems, solution based hp-adaptations offer the best promise. Adjoint-based adaptive methods have the capability of dynamically distributing computing resources to areas which are important for predicting engineering performance parameters, such as lift or drag. This thesis presents a robust and efficient adjoint-based adaptive high-order differential formulation for the compressible Navier-Stokes equations, which can rapidly determine an accurate estimate of an engineering output within a prescribed error threshold. The flux reconstruction (FR) or the correction procedure via reconstruction (CPR) method used in this work is a high-order differential formulation. We develop a parallel adjoint-based adaptive CPR solver which can work with any element-based error estimate and handle arbitrary discretization orders for mixed elements. First, a dual-consistent discrete form of the CPR method is derived. Then, an efficient and accurate adjoint-based error estimation method for the CPR method is developed and its accuracy and effectiveness are verified for the linear and non-linear partial differential equations (PDE). For anisotropic h-adaptations, we use a local output error sampling procedure to find the optimal refinement option. The current method has been applied to aerodynamic problems. Numerical tests show that significant savings in the number of DOFs can be achieved through the adjoint-based adaptation. Advisors/Committee Members: Wang, Z.J. (advisor), Farokhi, Saeed (cmtemember), Huang, Weizhang (cmtemember), Taghavi, Ray (cmtemember), Tu, Xuemin (cmtemember), Zheng, Zhongquan (cmtemember).

Subjects/Keywords: Aerospace engineering; Adaptive Method; Adjoint-based Adaptation; Computational Fluid Dynamics; High-order Method; Navier-Stokes Equations

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Shi, L. (2014). Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27533

Chicago Manual of Style (16^th Edition):

Shi, Lei. “Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.” 2014. Doctoral Dissertation, University of Kansas. Accessed April 16, 2021. http://hdl.handle.net/1808/27533.

MLA Handbook (7^th Edition):

Shi, Lei. “Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations.” 2014. Web. 16 Apr 2021.

Vancouver:

Shi L. Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2014. [cited 2021 Apr 16]. Available from: http://hdl.handle.net/1808/27533.

Council of Science Editors:

Shi L. Adaptive High-Order Differential Formulation for the Compressible Navier-Stokes Equations. [Doctoral Dissertation]. University of Kansas; 2014. Available from: http://hdl.handle.net/1808/27533

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