AJOU Central Library Repository: COMPUTATIONS OF OPTIMAL CONTROL PROBLEMS FOR THE STATIONARY BOUSSINESQ EQUATIONS

Graduate School of Ajou University Department of Mathematics 3. Theses(Master)

COMPUTATIONS OF OPTIMAL CONTROL PROBLEMS FOR THE STATIONARY BOUSSINESQ EQUATIONS

Abstract: 이 논문은 Boussinesq 방정식에 대한 온도를 이용한 최적제어 문제이다. 우리는 Neumann 경계조건과 soruce을 이용한 제어로서 유체의 소용돌이도를 줄이는 문제, 유체 추종문제, 그리고 온도 matching 문제에 대해 고려하였다. 우선 constrained 최소화 문제에 대한 최적 해의 존재성을 보이고 Lagrange multiplier 방법에 의해 optimality system을 유도한다. 이 optimality system의 유한요소근사법을 연구하였고 최적오차추정값을 얻었다. Gradient 방법을 이용하여 알고리즘을 짜고 그 수렴성을 연구하였다. 마지막으로 각각의 경우에 대하여 계산 결과를 수록하였다.

Alternative Abstract: This thesis deals with optimal control problems for steady state incompressible thermally convected flow. We considered vorticity minimization problem, flow matching problem, and temperature matching problem associated with the 2-D Boussinesq equations on a cavity with two kinds of temperature controls, i.e., Neumann boundary control, and Distributed control. These problems are first put into an appropriate mathematical formulation. Then, we state the constrained minimization problem and show the existence of the optimal solution and control. The optimality system of equations is derived by Lagrange multiplier techniques from which optimal solutions may be deduced. Finite element approximations of the optimality system are defined and optimal error estimates are derived. A simple iteration method is considered. Finally, some numerical results are given.

Appears in Collections:: Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)

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