Perturbation, approximation and optimal control of a system governed by the NavierStokes equations coupled to the heat equation
Abstract
A CauchyKowaleska system is used to approximate the NavierStokes equations coupled with the heat equation, giving variational formulations of the perturbed and nonperturbed problems. A finite difference approximation of these equations is also given. A specific numerical example is considered: the stability of a fluid in mechanical equilibrium but in thermodynamic nonequilibrium with attention given to the case of the twodimensional laminar flow induced by a temperature gradient in a closed cavity. CauchyKowaleska and finite difference approximations are then applied to the problem of the optimal control of the system of equations under consideration. The calculation of temperature distribution in the twodimensional laminar flow of a fluid in a square cavity is given as a numerical example.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1976
 Bibcode:
 1976PhDT........86C
 Keywords:

 Finite Difference Theory;
 Fluid Mechanics;
 NavierStokes Equation;
 Optimal Control;
 Perturbation Theory;
 Thermodynamics;
 Boussinesq Approximation;
 Convergence;
 Existence Theorems;
 Flow Stability;
 Laminar Flow;
 Nonequilibrium Thermodynamics;
 Numerical Stability;
 Tables (Data);
 Two Dimensional Flow;
 Variational Principles;
 Fluid Mechanics and Heat Transfer