Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation

ABSTRACT In this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier–Stokes equations.

[1]  Gianluigi Rozza,et al.  Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems , 2014 .

[2]  Pierre Ladevèze,et al.  Separated representations and PGD-based model reduction : fundamentals and applications , 2014 .

[3]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[4]  A. Patera,et al.  Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations , 2007 .

[5]  G. Rozza,et al.  A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods , 2016 .

[6]  Angelo Iollo,et al.  Iterative Methods for Model Reduction by Domain Decomposition , 2007, 0712.0691.

[7]  Angela Scardigli,et al.  Enabling of Large Scale Aerodynamic Shape Optimization Through POD-Based Reduced-Order Modeling and Free Form Deformation , 2018, Computational Methods in Applied Sciences.

[8]  J. Fröhlich,et al.  Hybrid LES/RANS methods for the simulation of turbulent flows , 2008 .

[9]  Angelo Iollo,et al.  Reduced Order Models at Work in Aeronautics and Medicine , 2014 .

[10]  Gianluigi Rozza,et al.  Certified reduced basis approximation for parametrized partial differential equations and applications , 2011 .

[11]  Karen Willcox,et al.  Proper orthogonal decomposition extensions for parametric applications in compressible aerodynamics , 2003 .

[12]  K. Carlson,et al.  Turbulent Flows , 2020, Finite Analytic Method in Flows and Heat Transfer.

[13]  F. Chinesta,et al.  A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .

[14]  Valentina Dolci,et al.  Proper Orthogonal Decomposition as Surrogate Model for Aerodynamic Optimization , 2016 .

[15]  James Demmel,et al.  Applied Numerical Linear Algebra , 1997 .

[16]  J. Samareh.  Aerodynamic Shape Optimization Based on Free-form Deformation , 2004 .

[17]  Angelo Iollo,et al.  Low-order models: optimal sampling and linearized control strategies , 2011 .

[18]  Sophie Papst,et al.  Computational Methods For Fluid Dynamics , 2016 .

[19]  Luca Heltai,et al.  Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes , 2016, Advanced Modeling and Simulation in Engineering Sciences.

[20]  Sivaguru S. Ravindran,et al.  Proper Orthogonal Decomposition in Optimal Control of Fluids , 1999 .

[21]  Wolf-Heinrich Hucho,et al.  Aerodynamics of Road Vehicles: From Fluid Mechanics to Vehicle Engineering , 2013 .

[22]  Gianluigi Rozza,et al.  Reduced Order Methods for Modeling and Computational Reduction , 2013 .

[23]  Gianluigi Rozza,et al.  Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives , 2016 .

[24]  Gianluigi Rozza,et al.  Model Order Reduction: a survey , 2016 .

[25]  L. Heltai,et al.  Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils , 2015 .

[26]  L. Sirovich.  Turbulence and the dynamics of coherent structures. II. Symmetries and transformations , 1987 .

[27]  Antonello Cogotti.  A Parametric Study on the Ground Effect of a Simplified Car Model , 1998 .

[28]  S. Ravindran.  A reduced-order approach for optimal control of fluids using proper orthogonal decomposition , 2000 .

[29]  Gianluigi Rozza,et al.  Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations , 2015 .

[30]  Stefan Menzel,et al.  On Shape Deformation Techniques for Simulation-Based Design Optimization , 2015 .

[31]  Nikolaus A. Adams,et al.  Introduction of a New Realistic Generic Car Model for Aerodynamic Investigations , 2012 .

[32]  Marco Attene,et al.  Recent Advances in Remeshing of Surfaces , 2008, Shape Analysis and Structuring.

[33]  Gianluigi Rozza,et al.  Free Form Deformation Techniques Applied to 3D Shape Optimization Problems , 2013 .

[34]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[35]  Steven Fortune,et al.  Voronoi Diagrams and Delaunay Triangulations , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[36]  Benjamin Peherstorfer,et al.  Dynamic data-driven reduced-order models , 2015 .

[37]  Nikolaus A. Adams,et al.  Investigation of Unsteady Flow Structures in the Wake of a Realistic Generic Car Model , 2011 .

[38]  Benjamin Peherstorfer,et al.  Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates , 2015, SIAM J. Sci. Comput..

[39]  J. Hesthaven,et al.  Certified Reduced Basis Methods for Parametrized Partial Differential Equations , 2015 .

[40]  Pierre Ladevèze,et al.  Separated Representations and PGD-Based Model Reduction , 2014 .

[41]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[42]  Bui Thanh Tan,et al.  Proper Orthogonal Decomposition Extensions and Their Applications in Steady Aerodynamics , 2003 .

[43]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[44]  P. Sagaut.  BOOK REVIEW: Large Eddy Simulation for Incompressible Flows. An Introduction , 2001 .

[45]  Gunther Ramm,et al.  Some salient features of the time - averaged ground vehicle wake , 1984 .

[46]  G. Rozza,et al.  Parametric free-form shape design with PDE models and reduced basis method , 2010 .

[47]  Michael J. Aftosmis,et al.  Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design , 2012 .

[48]  J. Delville,et al.  Proper Orthogonal Decomposition , 2003 .

[49]  Nadine Aubry,et al.  On The Hidden Beauty of the Proper Orthogonal Decomposition , 1991 .

[50]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[51]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..