Open Access
Volume 57, Number 3, May-June 2023
Page(s) 1691 - 1729
Published online 26 May 2023
  1. R. Aldbaissy, F. Hecht, G. Mansour and T. Sayah, A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity. Calcolo 55 (2018) 44. [CrossRef] [Google Scholar]
  2. K. Allali, A priori and a posteriori error estimates for Boussinesq equations. Int. J. Numer. Anal. Model. 2 (2005) 179–196. [Google Scholar]
  3. M.V. Balashov and M.O. Golubev, About the Lipschitz property of the metric projection in the Hilbert space. J. Math. Anal. App. 394 (2012) 545–551. [CrossRef] [Google Scholar]
  4. J. Boland and W. Layton, An analysis of the finite element method for natural convection problems. Numer. Methods Part. Differ. Equ. 6 (1990) 115–126. [CrossRef] [Google Scholar]
  5. J. Boland and W. Layton, Error analysis for finite element methods for steady natural convection problems. Numer. Funct. Anal. Optim. 11 (1990) 449–483. [CrossRef] [MathSciNet] [Google Scholar]
  6. S. Brenner and L.R. Scoot, The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics. Springer, New York, NY (2008). [CrossRef] [Google Scholar]
  7. B. Chandra and D.E. Smylie, A laboratory model of thermal convection under a central force field. Geophys. Fluid Dyn. 3 (1972) 211–224. [CrossRef] [Google Scholar]
  8. C. Egbers, W. Beyer, A. Bonhage, R. Hollerbach and P. Beltrame, The geoflow-experiment on ISS (part I): experimental preparation and design of laboratory testing hardware. Adv. Space Res. 32 (2003) 171–180. [CrossRef] [Google Scholar]
  9. E. Emmrich, Error of the two-step BDF for the incompressible Navier-Stokes problem. ESAIM: M2AN 38 (2004) 757–764. [CrossRef] [EDP Sciences] [Google Scholar]
  10. B. Futterer, N. Dahley and C. Egbers, Thermal electro-hydrodynamic heat transfer augmentation in vertical annuli by the use of dielectrophoretic forces through A.C.. Int. J. Heat Mass Transfer 93 (2016) 144–154. [CrossRef] [Google Scholar]
  11. S. Gawlok, P. Gerstner, S. Haupt, V. Heuveline, J. Kratzke, P. Lösel, K. Mang, M. Schmidtobreick, N. Schoch, N. Schween, J. Schwegler, C. Song and M. Wlotzka, HiFlow3 – technical report on release 2.0, Prepr. Ser. Eng. Math. Comput. Lab (2017). DOI: 10.11588/emclpp.2017.06.42879. [Google Scholar]
  12. P. Gerstner, Analysis and numerical approximation of dielectrophoretic force driven flow problems. Ph.D. thesis, Heidelberg University (2020). [Google Scholar]
  13. V. Girault and P.A. Raviart, Finite Element Approximation of the Navier–Stokes Equations. Lecture Notes in Mathematics. Springer-Verlag (1979). [CrossRef] [Google Scholar]
  14. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms. Springer Series in Computational Mathematics. Springer-Verlag (1986). [CrossRef] [Google Scholar]
  15. V. Girault, R.H. Nochetto and R. Scott, Stability of the finite element Stokes projection in W1,∞. C. R. Math. 338 (2004) 957–962. [CrossRef] [MathSciNet] [Google Scholar]
  16. J.G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 19 (1982) 275–311. [Google Scholar]
  17. J.G. Heywood and R. Rannacher, Finite-element approximation of the nonstationary Navier-Stokes problem. Part IV: error analysis for second-order time discretization. SIAM J. Numer. Anal. 27 (1990) 353–384. [Google Scholar]
  18. V. John, Finite Element Methods for Incompressible Flow Problems. Springer International Publishing (2016). [CrossRef] [Google Scholar]
  19. C. Kang and I. Mutabazi, Dielectrophoretic buoyancy and heat transfer in a dielectric liquid contained in a cylindrical annular cavity. J. Appl. Phys. 125 (2019) 184902. [CrossRef] [Google Scholar]
  20. C. Kang, A. Meyer, H.N. Yoshikawa and I. Mutabazi, Numerical simulation of circular Couette flow under a radial thermo-electric body force. Phys. Fluids 29 (2017) 114105. [CrossRef] [Google Scholar]
  21. C. Kang, A. Meyer, H.N. Yoshikawa and I. Mutabazi, Thermoelectric convection in a dielectric liquid inside a cylindrical annulus with a solid-body rotation. Phys. Rev. Fluids 4 (2019) 093502. [CrossRef] [Google Scholar]
  22. S.V. Malik, H.N. Yoshikawa, O. Crumeyrolle and I. Mutabazi, Thermo-electro-hydrodynamic instabilities in a dielectric liquid under microgravity. Acta Astronaut. 81 (2012) 563–569. [CrossRef] [Google Scholar]
  23. M. Meier, M. Jongmanns, A. Meyer, T. Seelig, C. Egbers and I. Mutabazi, Flow pattern and heat transfer in a cylindrical annulus under 1g and low-g conditions: experiments. Microgravity Sci. Technol. 30 (2018) 699–712. [CrossRef] [Google Scholar]
  24. A. Meyer, Active control of heat transfer by an electric field. Ph.D. thesis, Université du Havre (2017). [Google Scholar]
  25. A. Meyer, M. Jongmanns, M. Meier, C. Egbers and I. Mutabazi, Thermal convection in a cylindrical annulus under a combined effect of the radial and vertical gravity. C. R. Mécanique 345 (2017) 11–20. [CrossRef] [Google Scholar]
  26. A. Meyer, O. Crumeyrolle, I. Mutabazi, M. Meier, M. Jongmanns, M.-C. Renoult, T. Seelig and C. Egbers, Flow patterns and heat transfer in a cylindrical annulus under 1g and low-g conditions: theory and simulation. Microgravity Sci. Technol. 30 (2018) 653–662. [CrossRef] [Google Scholar]
  27. A. Meyer, M. Meier, M. Jongmanns, T. Seelig, C. Egbers and I. Mutabazi, Effect of the initial conditions on the growth of thermoelectric instabilities during parabolic flights. Microgravity Sci. Technol. 31 (2019) 11. [Google Scholar]
  28. I. Mutabazi, H.N. Yoshikawa, M.T. Fogaing, V. Travnikov, O. Crumeyrolle, B. Futterer and C. Egbers, Thermo-electro-hydrodynamic convection under microgravity: a review. Fluid Dyn. Res. 48 (2016) 061413. [CrossRef] [MathSciNet] [Google Scholar]
  29. R. Oyarzúa and P. Zúñiga, Analysis of a conforming finite element method for the Boussinesq problem with temperature-dependent parameters. J. Comput. Appl. Math. 323 (2017) 71–94. [Google Scholar]
  30. R. Oyarzúa, T. Qin and D. Schötzau, An exactly divergence-free finite element method for a generalized Boussinesq problem. IMA J. Numer. Anal. 34 (2013) 1104–1135. [Google Scholar]
  31. C.E. Pérez, J.-M. Thomas, S. Blancher and R. Creff, The steady Navier–Stokes/energy system with temperature-dependent viscosity – Part 2: the discrete problem and numerical experiments. Int. J. Numer. Methods Fluids 56 (2008) 91–114. [CrossRef] [Google Scholar]
  32. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition. Society for Industrial and Applied Mathematics (2003). [Google Scholar]
  33. P.W. Schröder and G. Lube, Stabilised dG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes. J. Comput. Phys. 335 (2017) 760–779. [CrossRef] [MathSciNet] [Google Scholar]
  34. P.W. Schröder, C. Lehrenfeld, A. Linke and G. Lube, Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations. SeMA J. 75 (2018) 629–653. [CrossRef] [MathSciNet] [Google Scholar]
  35. T. Seelig, A. Meyer, P. Gerstner, M. Meier, M. Jongmanns, M. Baumann, V. Heuveline and C. Egbers, Dielectrophoretic force-driven convection in annular geometry under Earth’s gravity. Int. J. Heat Mass Trans. 139 (2019) 386–398. [CrossRef] [Google Scholar]
  36. M. Smiszek, O. Crumeyrolle, I. Mutabazi and C. Egbers, Numerical simulation of thermoconvective instabilities of a dielectric liquid in a cylindrical annulus, in 59th International Austronautical Congress Glasgow in 59th International Austronautical Congress Glasgow 29/09-3/10 (2008). (2008). [Google Scholar]
  37. P.J. Stiles, Electro-thermal convection in dielectric liquids. Chem. Phys. Lett. 179 (1991) 311–315. [CrossRef] [Google Scholar]
  38. P.J. Stiles and M. Kagan, Stability of cylindrical Couette flow of a radially polarised dielectric liquid in a radial temperature gradient. Phys. A Stat. Mech. App. 197 (1993) 583–592. [CrossRef] [Google Scholar]
  39. M. Tabata and D. Tagami, Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients. Numer. Math. 100 (2005) 351–372. [Google Scholar]
  40. M. Takashima, Electrohydrodynamic instability in a dielectric fluid between two coaxial cylinders. Q. J. Mech. Appl. Math. 33 (1980) 93–103. [CrossRef] [Google Scholar]
  41. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis. AMS/Chelsea Publication (2001). [Google Scholar]
  42. V. Travnikov, O. Crumeyrolle and I. Mutabazi, Numerical investigation of the heat transfer in cylindrical annulus with a dielectric fluid under microgravity. Phys. Fluids 27 (2015) 054103. [CrossRef] [Google Scholar]
  43. V. Travnikov, O. Crumeyrolle and I. Mutabazi, Influence of the thermo-electric coupling on the heat transfer in cylindrical annulus with a dielectric fluid under microgravity. Acta Astronaut. 129 (2016) 88–94. [CrossRef] [Google Scholar]
  44. V. Travnikov, F. Zaussinger, P. Haun and C. Egbers, Influence of the dielectrical heating on the convective flow in the radial force field. Phys. Rev. E 101 (2020) 053106. [CrossRef] [PubMed] [Google Scholar]
  45. H.N. Yoshikawa, O. Crumeyrolle and I. Mutabazi, Dielectrophoretic force-driven thermal convection in annular geometry. Phys. Fluids 25 (2013) 024106. [CrossRef] [Google Scholar]
  46. F. Zaussinger, P. Haun, M. Neben, T. Seelig, V. Travnikov, C. Egbers, H. Yoshikawa and I. Mutabazi, Dielectrically driven convection in spherical gap geometry. Phys. Rev. Fluids 3 (2018) 093501. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you