Study on a BFC-Based POD-Galerkin Reduced-Order Model for the Unsteady-State Variable-Property Heat Transfer Problem

REFERENCES

• M. Loève , Probability Theory , van Nostrand , Princeton , NJ , 1955 .
   Google Scholar
• J. L. Lumley , The Structure of Inhomogeneous Turbulent Flows , Atmospheric Turbulence and Radio Wave Propagation , pp. 166 – 178 , 1967 .
   Google Scholar
• 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 , 1998 .
   Google Scholar
• L. Sirovich , Turbulence and the Dynamics of Coherent Structures, Quart. Appl. Math. , vol. 45, pp. 561–590, 1987.
   Web of Science ®Google Scholar
• P. Druault , J. Delville , and J. P. Bonnet , Proper Orthogonal Decomposition of the Mixing Layer Flow into Coherent Structures and Turbulent Gaussian Fluctuations , C. R. Acad. Sci. , vol. 333 , pp. 824 – 829 , 2005 .
   Google Scholar
• M. V. Tabib and 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 .
   Web of Science ®Google Scholar
• W. Kang and H. J. Sung , Large-Scale Structures of Turbulent Flows over an Open Cavity , J. Fluid Struct. , vol. 25 , pp. 1318 – 1333 , 2009 .
   Web of Science ®Google Scholar
• E. Liberge , Reduced Order Modelling Method via Proper Orthogonal Decomposition (POD) for Flow around an Oscillating Cylinder , J. Fluid Struct. , vol. 26 , pp. 292 – 311 , 2010 .
   Web of Science ®Google Scholar
• W. Zhu , Proper Orthogonal Decomposition Closure Models for Turbulent Flows: A Numerical Comparison , Comput. Meth. Appl. Mech. Eng. , vol. 237–240 , pp. 10 – 26 , 2012 .
   Web of Science ®Google Scholar
• R. Puragliesi and E. Leriche , Proper Orthogonal Decomposition of a Fully Confined Cubical Differentially Heated Cavity Flow at Rayleigh Number Ra = 109 , Comput. Fluids , vol. 61 , pp. 14 – 20 , 2012 .
   Web of Science ®Google Scholar
• G. Berkooz and E. S. Titi , Galerkin Projections and the Proper Orthogonal Decomposition for Equivariant Equations , Phys. Lett. A , vol. 174 , pp. 94 – 102 , 1993 .
   Web of Science ®Google Scholar
• D. Lucia and P. S. Beran , Projection Methods for Reduced Order Models of Compressible Flows , J. Comput. Phys. , vol. 188 , pp. 252 – 280 , 2003 .
   Web of Science ®Google Scholar
• T. A. Brenner , R. L. Fontenot , P. G. A. Cizmas , T. J. O'Brien , and R. W. Breault , Augmented Proper Orthogonal Decomposition for Problems with Moving Discontinuities , Powder Technol. , vol. 203 , pp. 78 – 85 , 2010 .
   Web of Science ®Google Scholar
• W. Kang , J. Z. Zhang , and K. L. Li , Nonlinear Galerkin Method for Dimension Reduction Using Proper Orthogonal Decomposition , J. Xi'an Jiaotong Univ. , vol. 45 , pp. 58 – 62 , 2011 .
   Google Scholar
• J. S. R. Anttonen , P. I. King , and P. S. Beran , POD-Based Reduced Order Models with Deforming Grids , Math. Comput. Model. , vol. 38 , pp. 41 – 62 , 2003 .
   Web of Science ®Google Scholar
• Y. Utturkar , B. Zhang , and W. Shyy , Reduced Order Description of Fluid Flow with Moving Boundaries by Proper Orthogonal Decomposition , Int. J. Heat Flow , vol. 26 , pp. 276 – 288 , 2005 .
   Web of Science ®Google Scholar
• S. Banerjee , J. V. Cole , and K. F. Jensen , Nonlinear Model Reduction Strategies for Rapid Thermal Processing Systems , IEEE Trans. Semiconduct. Mater. , vol. 11 , pp. 266 – 275 , 1988 .
   Google Scholar
• A. P. Raghupathy , U. Ghia , and K. Ghia , Boundary-Condition-Independent Reduced-Order Modeling of Complex 2D Objects by POD-Galerkin Methodology , Proc. 25th IEEE , Cincinnati , OH , pp. 208 – 215 , 2009 .
   Google Scholar
• S. S. Ravindran , Reduced Order Controllers for Control of Flow past an Airfoil , Int. J. Numer. Meth. Fluids , vol. 50 , pp. 531 – 554 , 2006 .
   Web of Science ®Google Scholar
• S. S. Ravindran , Control of Flow Separation over a Forward Facing Step by Model Reduction , Comput. Meth. Appl. Math. , vol. 191 , pp. 4599 – 4617 , 2002 .
   Web of Science ®Google Scholar
• 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 , 2006 .
   Web of Science ®Google Scholar
• 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 – 18 , 2004 .
   Web of Science ®Google Scholar
• H. M. Park and W. L. Lee , Feedback Control of Natural Convection , Comput. Meth. Appl. Math. , vol. 191 , pp. 1013 – 1028 , 2001 .
   Web of Science ®Google Scholar
• P. Ding , Application of the Reduced Order Model in the On-line Control of Glass Thickness and Solution of Heat Transfer Inverse Problems, Xi'an Jiaotong University, Xi'an, China, 2009.
   Google Scholar
• P. Ding and W. Q. Tao , Reduced Order Model Based Algorithm for Inverse Convection Heat Transfer Problem , J. Xi'an Jiaotong Univ. , vol. 43 , pp. 14 – 16 , 54 , 2009 .
   Google Scholar
• D. X. Han , B. Yu , G. J. Yu , Y. Zhao , and W. H. Zhang , Study on a BFC-Based POD-Galerkin ROM for the Steady-State Heat Transfer Problem , Int. J. Heat Mass Transf. , vol. 69 , pp. 1 – 5 , 2014 .
   Web of Science ®Google Scholar
• B. Yu , G. J. Yu , Z. Z. Cao , D. X. Han , and Q. 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 , vol. 63 , pp. 776 – 794 , 2012 .
   Web of Science ®Google Scholar
• W. Q. Tao , Numerical Heat Transfer, , 2nd ed. , pp. 453 – 463 , Xi'an Jiaotong University Press , Xi'an , China , 2001 .
   Google Scholar