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

Guoxing  Guan; Wenjing  Yan; Axia  Wang

doi:10.4236/jamp.2015.310158

Wenjing Yan¹^*, Axia Wang², Guoxing Guan¹

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

Cite this paper: Yan, W. , Wang, A. and Guan, G. (2015) A Numerical Method for Shape Optimal Design in the Oseen Flow with Heat Transfer. Journal of Applied Mathematics and Physics, 3, 1295-1307. doi: 10.4236/jamp.2015.310158.

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