05189nam 22007214a 450 991100668780332120200520144314.01-5231-2123-897866123491571-282-34915-50-19-157421-X(CKB)2560000000296379(EBL)3053556(OCoLC)922969630(SSID)ssj0000289002(PQKBManifestationID)11221424(PQKBTitleCode)TC0000289002(PQKBWorkID)10383679(PQKB)11632235(StDuBDS)EDZ0000075792(MiAaPQ)EBC3053556(MiAaPQ)EBC7038165(Au-PeEL)EBL7038165(EXLCZ)99256000000029637920091114d2010 uy 0engur|n|---|||||txtccrApplied shape optimization for fluids /Bijan Mohammadi, Olivier Pironneau2nd ed.Oxford ;New York Oxford University Pressc20101 online resource (292 p.)Numerical mathematics and scientific computationDescription based upon print version of record.0-19-954690-8 0-19-172048-8 Includes bibliographical references and index.Contents; 1 Introduction; 2 Optimal shape design; 2.1 Introduction; 2.2 Examples; 2.2.1 Minimum weight of structures; 2.2.2 Wing drag optimization; 2.2.3 Synthetic jets and riblets; 2.2.4 Stealth wings; 2.2.5 Optimal breakwater; 2.2.6 Two academic test cases: nozzle optimization; 2.3 Existence of solutions; 2.3.1 Topological optimization; 2.3.2 Suficient conditions for existence; 2.4 Solution by optimization methods; 2.4.1 Gradient methods; 2.4.2 Newton methods; 2.4.3 Constraints; 2.4.4 A constrained optimization algorithm; 2.5 Sensitivity analysis2.5.1 Sensitivity analysis for the nozzle problem2.5.2 Numerical tests with freefem++; 2.6 Discretization with triangular elements; 2.6.1 Sensitivity of the discrete problem; 2.7 Implementation and numerical issues; 2.7.1 Independence from the cost function; 2.7.2 Addition of geometrical constraints; 2.7.3 Automatic differentiation; 2.8 Optimal design for Navier-Stokes flows; 2.8.1 Optimal shape design for Stokes flows; 2.8.2 Optimal shape design for Navier-Stokes flows; References; 3 Partial differential equations for fluids; 3.1 Introduction; 3.2 The Navier-Stokes equations3.2.1 Conservation of mass3.2.2 Conservation of momentum; 3.2.3 Conservation of energy and and the law of state; 3.3 Inviscid flows; 3.4 Incompressible flows; 3.5 Potential flows; 3.6 Turbulence modeling; 3.6.1 The Reynolds number; 3.6.2 Reynolds equations; 3.6.3 The k - ε model; 3.7 Equations for compressible flows in conservation form; 3.7.1 Boundary and initial conditions; 3.8 Wall laws; 3.8.1 Generalized wall functions for u; 3.8.2 Wall function for the temperature; 3.8.3 k and ε; 3.9 Generalization of wall functions; 3.9.1 Pressure correction3.9.2 Corrections on adiabatic walls for compressible flows3.9.3 Prescribing ρ[sub(w)]; 3.9.4 Correction for the Reichardt law; 3.10 Wall functions for isothermal walls; References; 4 Some numerical methods for fluids; 4.1 Introduction; 4.2 Numerical methods for compressible flows; 4.2.1 Flux schemes and upwinded schemes; 4.2.2 A FEM-FVM discretization; 4.2.3 Approximation of the convection fluxes; 4.2.4 Accuracy improvement; 4.2.5 Positivity; 4.2.6 Time integration; 4.2.7 Local time stepping procedure; 4.2.8 Implementation of the boundary conditions4.2.9 Solid walls: transpiration boundary condition4.2.10 Solid walls: implementation of wall laws; 4.3 Incompressible flows; 4.3.1 Solution by a projection scheme; 4.3.2 Spatial discretization; 4.3.3 Local time stepping; 4.3.4 Numerical approximations for the k - ε equations; 4.4 Mesh adaptation; 4.4.1 Delaunay mesh generator; 4.4.2 Metric definition; 4.4.3 Mesh adaptation for unsteady flows; 4.5 An example of adaptive unsteady flow calculation; References; 5 Sensitivity evaluation and automatic differentiation; 5.1 Introduction; 5.2 Computations of derivatives; 5.2.1 Finite differences5.2.2 Complex variables methodExamining shape optimization problems for fluids, with the equations needed for their understanding and the simulation of these problems, this text introduces automatic differentiation approximate gradients, and automatic mesh refinement.Numerical mathematics and scientific computation.Fluid dynamicsMathematicsMathematical optimizationShape theory (Topology)Fluid dynamicsMathematics.Mathematical optimization.Shape theory (Topology)620.1/06/0151Mohammadi B1822931Pironneau Olivier306MiAaPQMiAaPQMiAaPQBOOK9911006687803321Applied shape optimization for fluids4389378UNINA