A Numerical Method for Shape Optimal Design in the Oseen Flow with Heat Transfer

Wenjing Yan^1*, Axia Wang², Guoxing Guan¹

¹School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China.
²School of Science, Chang’an University, Chang’an, China.

DOI: 10.4236/jamp.2015.310158                

Abstract

This paper is concerned with the optimal design of an obstacle located in the viscous and incompressible fluid which is driven by the steady-state Oseen equations with thermal effects. The structure of shape gradient of the cost functional is derived by applying the differentiability of a minimax formulation involving a Lagrange functional with a space parametrization technique. A gradient type algorithm is employed to the shape optimization problem. Numerical examples indicate that our theory is useful for practical purpose and the proposed algorithm is feasible.

Keywords

Shape Optimization, Oseen Equations, Shape Gradient, Minimax Principle, Convective Heat Transfer, Function Space Parametrization Technique

Conflicts of Interest

The authors declare no conflicts of interest.

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