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