Fluid Mechanics & Aerodynamics

Fluid Mechanics & Aerodynamics

Studying the Effect of Eddy Viscosity Closure on the Calibration of the DMD based Reduced-order Model to Predict the Long-term Behavior of Convection-Diffusion Equations

Document Type : Original Article

Authors
Mohammad Kazem Moayyedi 1
Zohreh Khakzari 2
Farshad sabaghzadeghan 2
1 Assistant Professor, Qom University, Qom, Iran
2 Master's student, University of Qom, Qom, Iran
Abstract
In this research, using the dynamic modes decomposition and using the basic concepts of the dynamical system, a data driven-physics informed reduced-order model has been developed for the viscous Burgers equation. Accordingly, based on the projection of the governing equation into the modal space, a reduced model is obtained according to the characteristics of the dominant modes. This model when used to simulate the field dynamics over a long time period, may become unstable. Therefore, an approach based on the concept of eddy viscosity closure has been used to stabilize the model behavior. This modification allows the reduced-order model to be a surrogate model of the original equation and predict the time evolution of the dynamical system with relative good accuracy. Comparing the results of the present reduced order model with the data obtained from the direct numerical simulations shows a high computational accuracy.
Keywords
Reduced Order Model
Viscous Burgers Equation
Dynamic Modes Decomposition
Eddy Viscosity Closure

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  1. Liang, Y. C., Lee, H. P., Lim, S. P., Lin, W. Z., Lee, K. H., and Wu, C. G. “Proper Orthogonal Decomposition and Its Applications—Part I: Theory”, Sound. Vib. Vol. 252, No. 3, pp. 527-544, 2002.
  2. LeGresley, P., and Alonso, J. “Investigation of Non-linear Projection for POD Based Reduced Order Models for Aerodynamics”, Aerospace. Eng. Reno, NV, USA, 2001.
  3. Fagiano, L., and Gati, R. “On the Order Reduction of the Radiative Heat Transfer Model for the Simulation of Plasma Arcs in Switchgear Devices”, Quant. Spectrosc. Ra. Vol. 169, pp. 58-78, 2016.
  4. Esfahanian, V., Ansari, A. B., and Torabi, F. “Simulation of Lead-Acid Battery Using Model Order Reduction” , Power. Sources. Vol. 279, pp. 246-305, 2015.
  5. Abreu, L. I., Cavalieri, A. V. G., Schlatter, P., Vinuesa, R., and Henningson, D. S. “Spectral Proper Orthogonal Decomposition and Resolvent Analysis of Near-Wall Coherent Structures in Turbulent Pipe Flows” , Fluid. Mech. Vol. 900, A. 11, 2020.
  6. Moayyedi, M.K., and Sabaghzadegan, F. “Development of Parametric and Time Dependent Reduced Order Model for Diffusion and Convection-Diffusion Problems Based on Proper Orthogonal Decomposition Method”, J. Mech. Eng. Vol. 53, No. 7, pp. 8-18, 2021. (In persian)
  7. Edwards, W. S., Tuckerman, L. S., Frienser, R. A., and Sorensen, D. C. “Krylov Methods for the Incompressible Navier-Stokes Equations”,
  8. Comp. Phys. Vol. 110, No. 1, pp. 82-102, 1994.
  9. Lehoucq, R. B., and Scott, J. A. “Implicitly Restarted Arnoldi Methods and Subspace Iteration” , J. Matrix. Anala. Vol. 23, pp. 551-562, 1997.
  10. Schmid, P. J. “Dynamic Mode Decomposition of Numerical and Experimental Data”, J. Fluid. Mech. Vol. 656, pp. 5-28, 2010.
  11. Rowley, C. W., Mezic, I., Bagheri, S., Schilatter, P., and Henningson, D. S. “Spectral Analysis of Nonlinear Flows” , Fluid. Mech. Vol. 641, pp. 115-127, 2009.
  12. Tomas, w.Muld., Efraimsson, G., and Henningson, D. S. “Flow Structures around a High-Speed Train Extracted Using Proper Orthogonal Decomposition and Dynamic Mode Decomposition”, Comput. Fluids. Vol. 57, pp. 87-97, 2012.
  13. Duke, D., Soria, J., and Honnery, D. “An Error Analysis of the Dynamic Mode Decomposition” , Fluids. Vol. 52, pp. 529-542, 2012.
  14. Seena, A., and Sung, H. J. “Spatiotemporal Representation of the Dynamic Modes in Turbulent Cavity Flows”, Int. J. Heat. Fluid. Flow. Vol. 44, pp. 1-13, 2013.
  15. Liu, H., Yan, C., Zhao, Y., and Qin, Y. “Analysis of Pressure Fluctuation in Transonic Cavity Flows Using Modal Decomposition,” Aerosp. Sci. Technol. Vol. 77, pp. 819-835, 2018.
  16. Hong, S. L., and Huang, G. P. “Introducing DMD Method to Study Dynamic Structures of Flow Separation With and Without Control,” Acta. Aeronaut. Astronaut. Sin. Vol. 38, No. 8, 2017.

 

  1. Li, C. Y., Tse, T. K. T., and Hu, G. “Dynamic Mode Decomposition on Pressure Flow Field Analysis: Flow Field Reconstruction, Accuracy, and Practical Significance”, Wind. Eng. Ind.
  2. Sun, C., Tian, T., Zu, X., Hua, O., and Du, Z. “Investigation of the Near Wake of a Horizontal-Axis Wind Turbine Model by Dynamic Mode Decomposition”, Vol. 227, 2021.
  3. Moayyedi, M.K., and Sabaghzadegan, F. “Reduced Order Model of Conduction Heat Transfer in a Solid Plate Based on Dynamic Mode Decomposition”, J. Mech. Eng. Vol. 37, No. 3, 2021. (In persian)
  4. Moayyedi, M.K., F. Sabetghadam, and M. Taeibi-Rahni. “Calibrated Low-dimensional POD Dynamical Model for Simulation of Unsteady Incompressible Flows”, Fluid Mechanics and Aerodynamics Journal. Vol. 1, No. 1, pp. 29-39, 2021. (In persian)
  5. Sabaghzadegan, F. “Development Reduced-Order Models for Convection-Diffusion Problems Based on Proper Orthogonal Decomposition and Dynamic Mode Decomposition”, Sc. Thesis, Department of Mechanical Engineering, University of Qom, 2019. (In persian)
Fluid Mechanics & Aerodynamics
Volume 11, Issue 1 - Serial Number 29
spring and summer
October 2022
Pages 83-96

  • Receive Date 27 February 2022
  • Revise Date 02 July 2022
  • Accept Date 11 July 2022
  • Publish Date 23 August 2022