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Reduced Order Model for Boundary Instigation of Burgers Equation of Turbulence Using Direct and Indirect Control Approaches | ||
| AUT Journal of Mechanical Engineering | ||
| مقاله 5، دوره 3، شماره 2، اسفند 2019، صفحه 173-186 اصل مقاله (2.52 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajme.2018.14240.5740 | ||
| نویسنده | ||
| Mohammad Kazem Moayyedi* | ||
| Department of Mechanical Engineering, University of Qom | ||
| چکیده | ||
| In this paper, a reduced order model is reconstructed for boundary control and excitation of the unsteady viscous Burgers equation. First, the standard reduced order proper orthogonal decomposition model, which has been extracted from the governing equations without control inputs, was evaluated and illustrated the satisfactory results in short time period. Two approaches are used to imply the effects of boundaries excitations and the related control routines. In the first, a source term was added to the governing equation of the reduced order dynamical system and was contributed as an expansion of the proper orthogonal decomposition modes without control input. For removing the inhomogeneities on the boundaries, the boundaries values are subtracted from all of the snapshots with an appropriate control input. The other approach is based on the rewriting of the diffusion term as an expanded form which contains the effect of boundaries values explicitly. In both approaches, the obtained reduced order models will contain two parts, the effect of system states and the influence of boundaries control functions. The results obtained from the reduced order model without the control inputs demonstrate a good agreement to the benchmark direct numerical simulations data and prove the high accuracy of the model. | ||
| کلیدواژه‌ها | ||
| Proper orthogonal decomposition؛ Galerkin projection؛ Reduced order model؛ Boundary control؛ Viscous Burger's equation | ||
| مراجع | ||
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[1] J.M. Burgers Mathematical Examples Illustrating Relations Occurring in the Theory of Turbulent Fluid Motion, Verh. Nederl. Akad. Wetensch. Afd. Natuurk, 1(17) (1939) 1–53.
[2] H.P. Breuer, F. Petruccione, Burger’s model of turbulence as a stochastic process, Journal of Physics A: Mathematical and General, 25(11) (1992) L661.
[3] W. Ea, Eijndenb, Eric Vanden, On the statistical solution of the Riemann equation and its implications for Burgers turbulence, Physics of Fluids, 11(8) (1999).
[4] J.a.K. Bec, K., Burgers Turbulence, Physics Reports, 447 (2007). 10.1016/j.physrep.2007.04.002.
[5] J.P.a.M.M. Bouchaud, Velocity fluctuations in forced Burgers turbulence, Physical Review, E 54(5) (1996) 5116-5121.
[6] I. Honkonen, Honkonen, Juha, Modelling turbulence via numerical functional integration using Burgers equation, in, 2018.
[7] C. Bayona, Baiges, Joan, Codina, Ramon, Variational multiscale approximation of the one-dimensional forced Burgers equation: The role of orthogonal subgrid scales in turbulence modeling, International Journal for Numerical Methods in Fluids, 86(5) (2018) 313-328.
[8] İ.A. T. Öziş, Similarity Solutions to Burgers’ Equation in Terms of Special Functions of Mathematical Physics, Acta Physica Polonica B, 48(7) (2017) 1349-1369.
[9] S.N.G. O. V. Rudenko, Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems, Mathematical Physics, 97(1) (2017) 95-98.
[10] J.A. Burns, Kang, Sungkwon, A control problem for Burgers’ equation with bounded input/output, Nonlinear Dynamics, 2(4) (1991) 235-262.
[11] G. Da Prato, Debussche, Arnaud, Control of the stochastic Burgers model of turbulence, SIAM journal on control and optimization, 37(4) (1999) 1123-1149.
[12] H. Choi, Temam, Roger, Moin, Parviz, Kim, John, Feedback control for unsteady flow and its application to the stochastic Burgers equation, Journal of Fluid Mechanics, 253 (1993) 509-543.
[13] J. Baker, Armaou A., and Christofides P.D., Nonlinear Control of Incompressible Fluid Flow: Application to Burgers’ Equation and 2D Channel Flow, Journal of Mathematical Analysis and Applications, 252(1) (2000) 230-255.
[14] B.G. Allan, A Reduced Order Model of the Linearized Incompressible Navier-Strokes Equations for the Sensor/ Actuator Placement Problem, NASA/CR-2000-210110 ICASE Report No. 2000-19, 2000.
[15] C.W. Rowley, Model reduction for fluids, using balanced proper orthogonal decomposition, International Journal of Bifurcation and Chaos, 15(03) (2005) 997-1013.
[16] S.S. Ravindran, A reduced‐order approach for optimal control of fluids using proper orthogonal decomposition, International journal for numerical methods in fluids, 34(5) (2000) 425-448.
[17] J.A. Atwell, Borggaard, Jeffrey T, King, Belinda B, Reduced order controllers for Burgers’ equation with a nonlinear observer, International Journal of Applied Mathematics and Computer Science, 11 (2001) 1311- 1330.
[18] M. Couplet, Basdevant, C, Sagaut, P, Calibrated reduced-order POD-Galerkin system for fluid flow modelling, Journal of Computational Physics, 207(1) (2005) 192-220.
[19] M. Taeibi-Rahni, Sabetghadam, F, Moayyedi, MK, Low-dimensional proper orthogonal decomposition modeling as a fast approach of aerodynamic data estimation, Journal of Aerospace Engineering, ASCE,23(1) (2009) 44-54.
[20] M.K. Moayyedi, Taeibi-Rahni, M., and, Sabetghadam, F., Accurate Low-dimensional Dynamical Model for Simulation of Unsteady Incompressible Flows, in: The 12th Fluid Dynamics Conference, Babol, Iran, 2009.
[21] P. Holmes, Lumley, John L, Berkooz, Gahl, Rowley, Clarence W, Turbulence, coherent structures, dynamical systems and symmetry, Cambridge university press, 2012.
[22] E. Hopf, The partial differential equation ut + uux = μuxx, Communications on Pure and Applied Mathematics, 3 (1950) 201–230.
[23] J.D. Cole, On a quasi-linear parabolic equation occurring in aerodynamics, Quarterly of applied mathematics, 9(3) (1951) 225-236.
[24] D. Cerná, and Finek, V., Numerical simulation of Burgers flow by wavelet method, (2007). | ||
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