Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 6
176
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

POD reduced-order model for steady laminar flow based on the body-fitted coordinate

, , , &
Pages 560-573 | Received 10 Nov 2016, Accepted 17 Feb 2017, Published online: 02 May 2017

References

  • J. L. Lumley, The Structure of Inhomogeneous Turbulent Flows, in A. M. Yaglom and V. I. Tatarski (eds.), Atmospheric Turbulence and Radio Wave Propagation, pp. 166–178, Nauka, Moscow, 1967.
  • N. Aubry, P. Holmes, J. L. Lumley, and E. Stone, The Dynamics of Coherent Structures in the Wall Region of a Turbulent Boundary Layer, J. Fluid Mech., vol. 192, pp. 115–173, 1988.
  • A. E. Deane, I. G. Kevrekidis, G. E. Karniadakis, and S. A. Orszag, Low–dimensional Models for Complex Geometry Flows: Application to Grooved Channels and Circular Cylinders, Phys. Fluids, vol. 3, pp. 2337–2354, 1991.
  • E. A. Christensen, J. N. Sørensen, M. Brøns, P. L. Christiansen, Low-Dimensional Representations of Early Transition in Rotating Fluid Flow, Theor. Comput. Fluid Dyn., vol. 5, pp. 259–267, 1993.
  • B. Podvin, P. L. Quéré, Low-Order Models for the Flow in a Differentially Heated Cavity, Phys. Fluids, vol. 13, pp. 3204–3214, 2001.
  • X. Ma, G. E. Karniadakis, A Low-Dimensional Model for Simulating Three-Dimensional Cylinder Flow, J. Fluid Mech., vol. 458, pp. 181–190, 2002.
  • N. Hasan, S. Sanghi, Proper Orthogonal Decomposition and Low-Dimensional Modeling of Thermally Driven Two-Dimensional Flow in a Horizontal Rotating Cylinder, J. Fluid Mech., vol. 573, pp. 265–295, 2007.
  • B. Podvin, A Proper-Orthogonal-Decomposition Based Model for the Wall Layer of a Turbulent Channel Flow, Phys. Fluids, vol. 21, 015111, 2009.
  • B. R. Noack, K. Afanasiev, M. Morzynski, G. Tadmor, and F. Thiele, A Hierarchy of Low-Dimensional Models for the Transient, and Post-Transient Cylinder Wake, J. Fluid Mech., vol. 497, pp.335–363, 2003.
  • D. Rempfer, On Low-Dimensional Galerkin Models for Fluid Flow, Theor. Comput. Fluid Dyn., vol. 14, pp.75–88, 2000.
  • V. L. Kalb and A. E. Deane, An Intrinsic Stabilization Scheme for Proper Orthogonal Decomposition Based Low-Dimensional Models, Phys. Fluids, vol. 19, 054106, 2007.
  • L. Perret, E. Collin, J. Delville, Polynomial Identification of POD Based Low-Order Dynamical System, J. Turbul., vol. 7, pp. 1–15, 2006.
  • B. Galletti, C. H. Bruneau, L. Zannetti, and A. Lollo, Low-Order Modelling of Laminar Flow Regimes Past a Confined Square Cylinder, J. Fluid Mech., vol. 503, pp. 161–170, 2004.
  • M. Couplet, C. Basdevant, P. Sagaut, Calibrated Reduced-Order POD-Galerkin System for Fluid Flow Modeling, J. Comput. Phys., vol. 207, pp. 192–220, 2005.
  • D. Amsallem, C. Farhat, Stabilization of Projection-Based Reduced-Order Models, Int. J. Numer. Methods Eng., vol. 91, pp. 358–377, 2012.
  • M. Bergmann, C. H. Bruneau, A. Iollo, Enablers for Robust POD Models, J. Comput. Phys., vol. 228, pp. 516–538, 2009.
  • M. Balajewicz, A New Approach to Model Order Reduction of the Navier–Stokes Equations, Thesis, Duke University, 2012.
  • H. M. Park, D. H. Cho, Low Dimensional Modeling of Flow Reactors, Int. J. Heat Mass Transfer, vol. 39, pp. 3311–3323, 1996.
  • W. Marquardt, Nonlinear Model Reduction for Optimization Based Control of Transient Chemical Processes, AIChE Symposium Series, New York, pp. 12–42, 2001.
  • P. G. Cizmas, A. Palacios, T. O’Brien, and M. Syamlal, Proper-Orthogonal Decomposition of Spatio-Temporal Patterns in Fluidized Beds, Chem. Eng. Sci., vol. 58, pp. 4417–4427, 2003.
  • M. V. Tabib, J. B. Joshi, Analysis of Dominant Flow Structures and Their Flow Dynamics in Chemical Process Equipment Using Snapshot Proper Orthogonal Decomposition Technique, Chem. Eng. Sci., vol. 63, pp. 3695–3715, 2008.
  • M. A. Singer, W. H. Green, Using Adaptive Proper Orthogonal Decomposition to Solve the Reaction–Diffusion Equation, Appl. Numer. Math., vol. 59, pp. 272–279, 2009.
  • M. Krasnyk, M. Mangold, S. Ganesan, and L. Tobiska, Numerical Reduction of a Crystallizer Model with Internal and External Coordinates by Proper Orthogonal Decomposition, Chem. Eng. Sci., vol. 70, pp. 77–86, 2012.
  • S. S. Ravindran, Reduced-Order Controllers for Control of Flow Past an Airfoil, Int. J. Numer. Methods Fluids, vol. 50, pp. 531–554, 2006.
  • S. S. Ravindran, Control of Flow Separation over a Forward-Facing Step by Model Reduction, Comput. Meth. Appl. Mech. Eng., vol. 191, pp. 4599–4617, 2002.
  • D. My-Ha, K. M. Lim, B. C. Khoo, and K. Willcox, Real-Time Optimization Using Proper Orthogonal Decomposition: Free Surface Shape Prediction due to Underwater Bubble Dynamics, Comput. Fluids, vol. 36, pp. 499–512, 2007.
  • M. Fogleman, J. L. Lumley, D. Rempfer, and D. Haworth, Application of the Proper Orthogonal Decomposition to Datasets of Internal Combustion Engine Flows, J. Turbul., vol. 5, pp. 1–3, 2004.
  • H. M. Park, W. J. Lee, Feedback Control of Natural Convection, Comput. Meth. Appl. Mech. Eng., vol. 191, pp. 1013–1028, 2001.
  • D. Han, B. Yu, G. Yu, Z. Yu, W. Zhang., Study on a BFC-Based POD-Galerkin ROM for the Steady-State Heat Transfer Problem, Int. J. Heat Mass Transfer, vol. 69, pp. 1–5, 2014.
  • D. Han, B. Yu, X. Zhang, Study on a BFC-Based POD-Galerkin Reduced-Order Model for the Unsteady-State Variable-Property Heat Transfer Problem, Numer. Heat Tranfer B Fund., vol. 65, pp. 256–281, 2015.
  • B. Yu, G. Yu, Z. Cao, D. Han, and Q. Shao, Fast Calculation of the Soil Temperature Field Around a Buried Oil Pipeline Using a Body-Fitted Coordinates-Based POD-Galerkin Reduced-Order Model, Numer. Heat Transfer A Appl., vol. 63, pp. 776–794, 2013.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.