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  • 1.
    Amoignon, Olivier
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Adjoint-based aerodynamic shape optimization2003Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    An adjoint system of the Euler equations of gas dynamics is derived in order to solve aerodynamic shape optimization problems with gradient-based methods. The derivation is based on the fully discrete flow model and involves differentiation and transposition of the system of equations obtained by an unstructured and node-centered finite-volume discretization. Solving the adjoint equations allows an efficient calculation of gradients, also when the subject of optimization is described by hundreds or thousands of design parameters.

    Such a fine geometry description may cause wavy or otherwise irregular designs during the optimization process. Using the one-to-one mapping defined by a Poisson problem is a known technique that produces smooth design updates while keeping a fine resolution of the geometry. This technique is extended here to combine the smoothing effect with constraints on the geometry, by defining the design updates as solutions of a quadratic programming problem associated with the Poisson problem.

    These methods are applied to airfoil shape optimization for reduction of the wave drag, that is, the drag caused by gas dynamic effects that occur close to the speed of sound. A second application concerns airfoil design optimization to delay the laminar-to-turbulent transition point in the boundary layer in order to reduce the drag. The latter application has been performed by the author with collaborators, also using gradient-based optimization. Here, the growth of convectively unstable disturbances are modeled by successively solving the Euler equations, the boundary layer equations, and the parabolized stability equations.

  • 2.
    Amoignon, Olivier
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Moving mesh adaptation scheme for aerodynamic shape optimization2006Report (Other academic)
  • 3.
    Amoignon, Olivier
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Numerical Methods for Aerodynamic Shape Optimization2005Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances.

    When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries.

    Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation.

    In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme.

    The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

    List of papers
    1. Adjoint of a median-dual finite-volume scheme: Application to transonic aerodynamic shape optimization
    Open this publication in new window or tab >>Adjoint of a median-dual finite-volume scheme: Application to transonic aerodynamic shape optimization
    2006 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-013
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-80174 (URN)
    Projects
    Design Optimization
    Available from: 2007-09-16 Created: 2007-09-16 Last updated: 2018-01-13Bibliographically approved
    2. Shape optimization for delay of laminar-turbulent transition
    Open this publication in new window or tab >>Shape optimization for delay of laminar-turbulent transition
    Show others...
    2006 (English)In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 44, p. 1009-1024Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-80640 (URN)10.2514/1.12431 (DOI)000237492000010 ()
    Projects
    Design Optimization
    Available from: 2007-01-31 Created: 2007-01-31 Last updated: 2018-01-13Bibliographically approved
    3. Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization
    Open this publication in new window or tab >>Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization
    2007 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 36, p. 1119-1136Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-22158 (URN)10.1016/j.compfluid.2006.11.002 (DOI)000246537700008 ()
    Projects
    Design Optimization
    Available from: 2007-04-16 Created: 2007-04-16 Last updated: 2018-01-12Bibliographically approved
    4. Moving mesh adaptation scheme for aerodynamic shape optimization
    Open this publication in new window or tab >>Moving mesh adaptation scheme for aerodynamic shape optimization
    2006 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-014
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-80175 (URN)
    Projects
    Design Optimization
    Available from: 2007-09-17 Created: 2007-09-17 Last updated: 2018-01-13Bibliographically approved
  • 4.
    Amoignon, Olivier
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Berggren, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Adjoint of a median-dual finite-volume scheme: Application to transonic aerodynamic shape optimization2006Report (Other academic)
  • 5.
    Amoignon, Olivier
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Berggren, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Discrete adjoint-based shape optimization for an edge-based finite-volume solver2003In: Computational Fluid and Solid Mechanics: 2003, Elsevier Science , 2003, p. 2190-2193Conference paper (Refereed)
  • 6.
    Amoignon, Olivier
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Pralits, Jan
    Hanifi, Ardeshir
    Berggren, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Henningson, Dan
    Shape optimization for delay of laminar-turbulent transition2006In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 44, p. 1009-1024Article in journal (Refereed)
  • 7. Jakobsson, Stefan
    et al.
    Amoignon, Olivier
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization2007In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 36, p. 1119-1136Article in journal (Refereed)
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