A flexible symmetry-preserving Galerkin/POD reduced order model applied to a convective instability problem

Allgower, 2003, Introduction to numerical continuation methods, vol. 45 Alonso, 2009, A method to generate computationally efficient reduced order models, Comput Meth Appl Mech Eng, 198, 2683, 10.1016/j.cma.2009.03.012 Alonso, 2010, Reduced order model for viscous aerodynamic flow past an airfoil, AIAA J, 48, 1946, 10.2514/1.J050153 Alonso, 2012, Reduced-order modeling of three-dimensional external aerodynamic flows, J Aerospace Eng, 25, 588, 10.1061/(ASCE)AS.1943-5525.0000148 Aranson, 2002, The world of the complex Ginzburg–Landau equation, Rev Mod Phys, 74, 100, 10.1103/RevModPhys.74.99 Aubry, 1993, Preserving symmetries in the proper orthogonal decomposition, SIAM J Sci Comput, 14, 483, 10.1137/0914030 Bache, 2010, Model reduction in the back step fluid-thermal problem with variable geometry, Int J Thermal Sci, 49, 2376, 10.1016/j.ijthermalsci.2010.07.013 Bénard, 1900, Les tourbillons cèllulaires dans une nappe liquide, Rev Gen Sci Pures Appl Bull Assoc, 11, 1261 Bernardi, 1991 Braconnier, 2011, Towards an adaptive POD/SVD surrogate model for aeronautic design, Comput Fluids, 40, 195, 10.1016/j.compfluid.2010.09.002 Canuto, 1988 Chaturantabut, 2010, Nonlinear model reduction via discrete empirical interpolation, SIAM J Sci Comput, 32, 2737, 10.1137/090766498 Couplet, 2005, Calibrated reduced-order POD-Galerkin system for fluid flow modelling, J Comput Phys, 207, 192, 10.1016/j.jcp.2005.01.008 Crawford, 1991, Symmetry and symmetry-breaking bifurcations in fluid dynamics, Annu Rev Fluid Mech, 23, 341, 10.1146/annurev.fl.23.010191.002013 Davies, 2001 Deparis, 2009, Reduced basis method for multi-parameter-dependent steady Navier–Stokes equations: applications to natural convection in a cavity, J Comput Phys, 228, 4359, 10.1016/j.jcp.2009.03.008 Dowell, 2001, Modeling of fluid-structure interaction, Annu Rev Fluid Mech, 33, 445, 10.1146/annurev.fluid.33.1.445 Foias, 1988, Inertial manifolds for nonlinear evolutionary equations, J Differ Eqations, 73, 309, 10.1016/0022-0396(88)90110-6 Foias, 1988, Inertial manifolds for the Kuramoto–Sivashinsky equation and an estimate of their lowest dimension, J Math Pures Appl, 67, 197 Golub, 1996 Golubitsky, 1984, Symmetries and pattern selection in Rayleigh–Bénard convection, Physica D, 10, 249, 10.1016/0167-2789(84)90179-9 Haragus, 2010 Herrero, 2013, RB (Reduced Basis) applied to RB (Rayleigh–Bénard), Comput Methods Appl Mech Eng, 261–262, 132, 10.1016/j.cma.2013.02.018 Ilak, 2010, Model reduction of the nonlinear complex Ginzburg–Landau equation, SIAM J Appl Dyn Syst, 9, 1284, 10.1137/100787350 Jolly, 1993, Bifurcation computations on an approximate inertial manifold for the 2D Navier–Stokes equations, Physica D, 63, 8, 10.1016/0167-2789(93)90143-O Kunisch, 2003, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics, SIAM J Numer Anal, 40, 492, 10.1137/S0036142900382612 Kutnetsov, 2004, Elements of applied bifurcation theory, vol. 112 Lassila, 2014, Model order reduction in fuid dynamics: challenges and perspectives, vol. 9, 235 LeGresley PA, Alonso JJ. Investigation of non-linear projection for POD based reduced order models for aerodynamics. AIAA paper 2001-0926. 39th AIAA aerospace sciences meeting & exhibit; 2001. Lieu, 2006, Reduced-order fluid/structure modeling of a complete aircraft configuration, Comput Meth Appl Mech Eng, 195, 5730, 10.1016/j.cma.2005.08.026 Lucia, 2004, Reduced-order modelling: new approaches for computations physics, Prog Aerosp Sci, 40, 51, 10.1016/j.paerosci.2003.12.001 Manzoni, 2014, An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows, ESAIM Math Model Numer Anal, 48, 1199, 10.1051/m2an/2014013 Pla, 2008, Bifurcation phenomena in a convection problem with temperature dependent viscosity at low aspect ratio, Physica D, 238, 572, 10.1016/j.physd.2008.12.015 Promislow, 1991, Localization and approximation of attractors for the Ginzburg–Landau equation, J Dyn Differ Equations, 3, 491, 10.1007/BF01049097 Prud’homme, 2002, Reliable real-time solution of parametrized partial differential equations: reduced-basis output bounds methods, J Fluids Eng, 124, 70, 10.1115/1.1448332 Rapún, 2010, Reduced order models based on local POD plus Galerkin projection, J Comput Phys, 229, 3046, 10.1016/j.jcp.2009.12.029 Rempfer, 2003, Low-dimensional modeling and numerical simulation of transition in simple shear flows, Annu Rev Fluid Mech, 35, 229, 10.1146/annurev.fluid.35.030602.113908 Richter, 1983, Heat transfer and horizontally averaged temperature of convection with large viscosity variations, J Fluid Mech, 129, 173, 10.1017/S0022112083000713 Ryckelynck, 2009, Hyper-reduction of mechanical models involving internal variables, Int J Numer Methods Eng, 77, 75, 10.1002/nme.2406 Robinson, 2002, Computing inertial manifolds, Discrete Cont Dyn Syst, 8, 815, 10.3934/dcds.2002.8.815 Rozza, 2008, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Arch Comput Methods Eng, 15, 229, 10.1007/s11831-008-9019-9 Shah, 2006, A symmetry preserving singular value decomposition, SIAM J Matrix Anal Appl, 28, 749, 10.1137/050646676 Shah M. A symmetry preserving singular value decomposition. PhD Thesis. CAAM, Rice University, TR07-06; 2007. Shah, 2010, Best non-spherical symmetric low rank approximation, SIAM J Matrix Anal Appl, 31, 1019, 10.1137/080732808 Siegel, 2008, Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition, J Fluid Mech, 610, 1, 10.1017/S0022112008002115 Sirisup, 2005, Stability and accuracy of periodic flow solutions obtained by a POD-penalty method, Physica D, 202, 218, 10.1016/j.physd.2005.02.006 Sirisup, 2005, Equations-free/Galerkin-free POD assisted computation of incompressible flows, J Comput Phys, 207, 568, 10.1016/j.jcp.2005.01.024 Strikwerda, 1989 Terragni, 2011, Local POD plus Galerkin projection in the unsteady lid-driven cavity problem, SIAM J Sci Comput, 33, 3538, 10.1137/100816006 Terragni, 2012, On the use of POD-based ROMs to analyze bifurcations in some dissipative systems, Physica D, 241, 1393, 10.1016/j.physd.2012.04.009 Terragni, 2014, Construction of bifurcation diagrams using POD on the fly, SIAM J Appl Dyn Syst, 13, 330, 10.1137/130927267 Thomas, 2010, Using automatic differentiation to create a nonlinear reduced-order-model aerodynamic solver, AIAA J, 48, 19, 10.2514/1.36414 Zienkiewicz, 1971