Shape optimization in the Navier-Stokes flow with thermal effects. (English) Zbl 1308.76075
Summary: We consider the shape optimization problem of a body immersed in the incompressible fluid governed by Navier-Stokes equations coupling with a thermal model. Based on the continuous adjoint method, we formulate and analyze the shape optimization problem. Then we derive the structure of shape gradient for the cost functional by using the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape optimization problem. Finally, numerical examples demonstrate the feasibility and effectiveness of the proposed algorithm.
MSC:
76D05 | Navier-Stokes equations for incompressible viscous fluids |
76D55 | Flow control and optimization for incompressible viscous fluids |
76R50 | Diffusion |
65K10 | Numerical optimization and variational techniques |
49Q10 | Optimization of shapes other than minimal surfaces |
74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
74P10 | Optimization of other properties in solid mechanics |
80A20 | Heat and mass transfer, heat flow (MSC2010) |
Keywords:
shape optimization; computational fluid dynamics; shape gradient; Navier-Stokes equations; minimax principle; convective heat transferReferences:
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