Applied Shape Optimization for Fluids

By Bijan Mohammadi, Olivier Pironneau. 2001

597 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/035ac6e840595d8605ec7f317e8c31f8d99438c5

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Citations in the corpus

Stacking sequence and shape optimization of laminated composite plates via a level-set method (2016, methodology): “As a response to this challenge, several techniques for size, shape and topology optimization have successfully been developed and applied to aircraft design [4, 9, 26, 27, 50, 61, 62].”
CONTROLLABILITY OF PARTIAL DIFFERENTIAL EQUATIONS AND ITS SEMI-DISCRETE APPROXIMATIONS (2006, background): “On the other hand, it has been observed that, for the solution of a lot of optimal design problems, the first strategy is preferable; see for instance [167] and [181].”
Levenberg–Marquardt level set methods for inverse obstacle problems (2004, background): “[ 30 ]). This approach and a generalization to general gradient ∞ows (cf.”
SHAPE OPTIMIZATION IN FLUID MECHANICS (2004, methodology): “Analysis suggests using a fourth-order operator (Mohammadi & Pironneau 2001).”
Aerodynamic Shape Optimization Using First and Second Order Adjoint and Direct Approaches (2008, methodology): “It is proved, [89, 90], using some simple cases, that this approach leads to sensitivity derivatives of at least the right sign.”
Shape optimization for viscous flows by reduced basis methods and free‐form deformation (2012, methodology): “Since shape representation is highly specific problem-dependent, various methods have been proposed; a classical approach in geometrical shape optimization is the so-called local boundary variation technique [2, 27], while the most common shape representation adopted in parametric shape optimization”
Level set topology optimization of fluids in Stokes flow (2009, result): “The derivation is therefore presented here even though the result has been derived previously [48].”
A comparative study of the performance of high resolution advection schemes in the context of data assimilation (2006, unknown): “In aerodynamics applications, such as minimization of drag, maximization of lift (as target functionals) are often performed by considering the geometry of the immersed body in the uid as the control variable, which is called shape optimization [31], for other applications and details, see Reference”
Structural optimization using sensitivity analysis and a level-set method (2004, unknown): “[6,14], or Chapter 5 in [23]).”
Free-form-deformation parameterization for multilevel 3D shape optimization in aerodynamics (2003, methodology): “In the literature [32], one might choose from: - explicit deformation: we prescribe the deformation to apply to each mesh node (Marocco [31]), knowing the shape skin deformation; the deformation for a node is proportional to its distance to the shape.”
The turnpike property in finite-dimensional nonlinear optimal control (2014, unknown): “Indeed, both in elasticity (see [3]) and aeronautics (see [32, 39]), most often, optimal shape designs or optimal materials are determined on the basis of a steady-state modeling.”
A topology optimization method based on the level set method incorporating a fictitious interface energy (2010, background): “Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method.”
Shape and topology optimization based on the phase field method and sensitivity analysis (2010, methodology): “Details of the history and methodologies of various proposed methods can be found in comprehensive reviews and textbooks [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13].”