Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 80, 2021 - Issue 3-4
217
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Numerical investigations on model order reduction to SEM based on POD-DEIM to linear/nonlinear heat transfer problems

, , , &
Pages 39-52 | Received 20 Feb 2021, Accepted 28 May 2021, Published online: 08 Jul 2021

References

  • T. Gjesdal, C. E. Wasberg and B. A. P. Reif, “Spectral element benchmark simulations of natural convection in two-dimensional cavities,” Int. J. Numer. Meth. Fluids, vol. 50, no. 11, pp. 1297–1319, 2006. DOI: 10.1002/fld.1121.
  • Y. Wang and G. Qin, “An improved time-splitting method for simulating natural convection heat transfer in a square cavity by legendre spectral element approximation,” Comput.Fluids, vol. 174, pp. 122–134, 2018. DOI: 10.1016/j.compfluid.2018.07.013.
  • Y. Wang, G. Qin, K. K. Tamma and Y. Geng, “Accurate solution for natural convection around single and tandem circular cylinders inside a square enclosure using sem,” Numer. Heat Transf. Part A Appl., vol. 75, no. 9, pp. 579–597, 2019. DOI: 10.1080/10407782.2019.1608778.
  • C. Galletti, A. Mariotti, L. Siconolfi, R. Mauri and E. Brunazzi, “Numerical investigation of flow regimes in t-shaped micromixers: Benchmark between finite volume and spectral element methods,” Can. J. Chem. Eng., vol. 97, no. 2, pp. 528–541, 2019. DOI: 10.1002/cjce.23321.
  • R. Pinnau, “Model reduction via proper orthogonal decomposition,” in: Model Order Reduction: Theory, Research Aspects and Applications, Springer-Verlag Berlin Heidelberg, 2008, pp. 95–109.
  • J. Lumley, “Atmospheric turbulence and radio wave propagation,” in: The Structure of Inhomogeneous Turbulent Flows, Moscow: Nauka, 1967, pp. 166–178.
  • M. Gunzburger, N. Jiang and M. Schneier, “An ensemble-proper orthogonal decomposition method for the nonstationary Navier-Stokes equations,” SIAM J. Numer. Anal., vol. 55, no. 1, pp. 286–304, 2017. DOI: 10.1137/16M1056444.
  • M. Dehghan and M. Abbaszadeh, “Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier-Stokes equation,” Comput. Methods Appl. Mech. Eng., vol. 311, pp. 856–888, 2016. DOI: 10.1016/j.cma.2016.09.008.
  • X. Zhang and H. Xiang, “A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problems,” Int. J. Heat Mass Transf., vol. 84, pp. 729–739, 2015. DOI: 10.1016/j.ijheatmasstransfer.2015.01.008.
  • F. Selimefendigil and H. F. Öztop, “Numerical study and POD-based prediction of natural convection in a ferrofluids–filled triangular cavity with generalized neural networks,” Numer. Heat Transf. Part A Appl., vol. 67, no. 10, pp. 1136–1161, 2015. DOI: 10.1080/10407782.2014.955345.
  • R. Ghosh and Y. Joshi, “Rapid temperature predictions in data centers using multi-parameter proper orthogonal decomposition,” Numer. Heat Transf. Part A Appl., vol. 66, no. 1, pp. 41–63, 2014. DOI: 10.1080/10407782.2013.869090.
  • D. Ahlman, F. Söderlund, J. Jackson, A. Kurdila and W. Shyy, “Proper orthogonal decomposition for time-dependent lid-driven cavity flows,” Numer. Heat Transf. Part B Fundamentals, vol. 42, no. 4, pp. 285–306, 2002. DOI: 10.1080/10407790190053950.
  • A. Fic, R. A. Białecki and A. J. Kassab, “Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method,” Numer. Heat Transf. Part B Fundamentals, vol. 48, no. 2, pp. 103–124, 2005. DOI: 10.1080/10407790590935920.
  • R. Bennacer and K. Sefiane, “Proper orthogonal decomposition (POD) analysis of flow structure in volatile binary droplets,” Int. Commun. Heat Mass Transf., vol. 71, pp. 172–175, 2016. DOI: 10.1016/j.icheatmasstransfer.2015.12.036.
  • J. Chen, D. Han, B. Yu, D. Sun and J. Wei, “A POD-Galerkin reduced-order model for isotropic viscoelastic turbulent flow,” Int. Commun. Heat Mass Transf., vol. 84, pp. 121–133, 2017. DOI: 10.1016/j.icheatmasstransfer.2017.04.010.
  • Z. Luo and S. Jin, “A reduced-order extrapolation spectral-finite difference scheme based on the POD method for 2D second-order hyperbolic equations,” Math. Model. Anal., vol. 22, no. 5, pp. 569–586, 2017. DOI: 10.3846/13926292.2017.1334714.
  • Z. Luo and W. Jiang, “A reduced-order extrapolated Crank-Nicolson finite spectral element method for the 2D non-stationary Navier-Stokes equations about vorticity-stream functions,” Appl. Numer. Math., vol. 147, pp. 161–173, 2020. DOI: 10.1016/j.apnum.2019.08.007.
  • S. Chaturantabut and D. C. Sorensen, “Nonlinear model reduction via discrete empirical interpolation,” SIAM J. Sci. Comput., vol. 32, no. 5, pp. 2737–2764, 2010. DOI: 10.1137/090766498.
  • S. Chaturantabut and D. C. Sorensen, “Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media,” Math. Comput. Model. Dyn. Syst., vol. 17, no. 4, pp. 337–353, 2011. DOI: 10.1080/13873954.2011.547660.
  • R. Ştefănescu and I. M. Navon, “POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model,” J. Comput. Phys., vol. 237, pp. 95–114, 2013. DOI: 10.1016/j.jcp.2012.11.035.
  • R. Ştefănescu, A. Sandu and I. M. Navon, “POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation,” J. Comput. Phys., vol. 295, pp. 569–595, 2015. DOI: 10.1016/j.jcp.2015.04.030.
  • M. Barrault, Y. Maday, N. C. Nguyen and A. T. Patera, “An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations,” Comptes Rendus Math., vol. 339, no. 9, pp. 667–672, 2004. DOI: 10.1016/j.crma.2004.08.006.
  • S. Masuri, M. Sellier, X. Zhou and K. K. Tamma, “Design of order-preserving algorithms for transient first-order systems with controllable numerical dissipation,” Int. J. Numer. Meth. Eng., vol. 88, no. 13, pp. 1411–1448, 2011. DOI: 10.1002/nme.3228.
  • M. Shimada, S. Masuri and K. Tamma, “A novel design of an isochronous integration [iIntegration] framework for first/second order multidisciplinary transient systems,” Int. J. Numer. Meth. Eng., vol. 102, no. 3-4, pp. 867–891, 2015. DOI: 10.1002/nme.4715.
  • K. K. Tamma and S. U. Masuri, “A novel extension of GS4-1 time integrator to fluid dynamics type non-linear problems with illustrations to Burgers’ equation,” Int. J. Numer. Methods Heat Fluid Flow, vol. 26, no. 6, pp. 1634–1660, 2016. DOI: 10.1108/HFF-04-2015-0155.
  • T. Xue, X. Zhang and K. K. Tamma, “Generalized heat conduction model involving imperfect thermal contact surface: Application of the GSSSS-1 differential-algebraic equation time integration,” Int. J. Heat Mass Transf., vol. 116, pp. 889–896, 2018. DOI: 10.1016/j.ijheatmasstransfer.2017.09.081.
  • T. Xue, X. Zhang and K. K. Tamma, “A two-field state-based peridynamic theory for thermal contact problems,” J. Comput. Phys., vol. 374, pp. 1180–1195, 2018. DOI: 10.1016/j.jcp.2018.08.014.
  • D. Maxam, R. Deokar and K. K. Tamma, “A unified computational methodology for dynamic thermoelasticity with multiple subdomains under the GSSSS framework involving differential algebraic equation systems,” J. Therm Stresses, vol. 42, no. 1, pp. 163–184, 2019. DOI: 10.1080/01495739.2018.1536869.
  • K. K. Tamma, X. Zhou and D. Sha, “The time dimension: A theory towards the evolution, classification, characterization and design of computational algorithms for transient/dynamic applications,” ARCO, vol. 7, no. 2, pp. 67–290, 2000. DOI: 10.1007/BF02736209.
  • K. K. Tamma, J. Har, X. Zhou, M. Shimada and A. Hoitink, “An overview and recent advances in vector and scalar formalisms: Space/time discretizations in computational dynamics–a unified approach,” Arch. Comput. Methods Eng., vol. 18, no. 2, pp. 119–283, 2011. DOI: 10.1007/s11831-011-9060-y.
  • Y. Wang and G. Qin, “Accurate numerical simulation for non-darcy double-diffusive mixed convection in a double lid-driven porous cavity using sem,” Numer. Heat Transf. Part A Appl., vol. 75, no. 9, pp. 598–615, 2019. DOI: 10.1080/10407782.2019.1608764.
  • R. Deokar and K. K. Tamma, “A novel model order reduction framework via staggered reduced basis space-time finite elements in linear first order transient systems,” Int. J. Heat Mass Transf., vol. 117, pp. 991–1005, 2018. DOI: 10.1016/j.ijheatmasstransfer.2017.10.039.
  • D. Maxam, R. Deokar and K. K. Tamma, “The applicability of model order reduction based on proper orthogonal decomposition to problems in dynamic thermoelasticity with multiple subdomains,” J. Therm. Stresses, vol. 42, no. 6, pp. 744–768, 2019. DOI: 10.1080/01495739.2019.1581720.
  • R. Deokar, M. Shimada, C. Lin and K. K. Tamma, “On the treatment of high-frequency issues in numerical simulation for dynamic systems by model order reduction via the proper orthogonal decomposition,” Comput. Methods Appl. Mech. Eng., vol. 325, pp. 139–154, 2017. DOI: 10.1016/j.cma.2017.07.003.

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.