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Application of the sequential gradient-restoration algorithm to thermal convective instability problems

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Abstract

The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.

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The authors acknowledge valuable discussions with Dr. A. Miele.

Communicated by K. G. Guderley

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Lam, T.T., Bayazitoglu, Y. Application of the sequential gradient-restoration algorithm to thermal convective instability problems. J Optim Theory Appl 49, 47–63 (1986). https://doi.org/10.1007/BF00939247

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Key Words

  • Convective instability
  • thermal instability
  • Benard problem
  • linear stability theory
  • optimal control
  • numerical methods
  • computing methods
  • gradient methods
  • gradient-restoration algorithm
  • sequential gradient-restoration algorithm