Applied shape optimization for fluids (Q2703821)

The book deals with the problem of shape optimization in fluid dynamics, a very important problem for practical design of planes, cars, turbines, etc. In this book the optimal shape design is carefully presented from both theoretical and practical points of view. The main target of the book is the full airplane shape optimization, based on Navier-Stokes equations with a joint adequate \(k\)-\(\varepsilon\) turbulence model. The main tool in this approach is the use of algorithms of gradient type. The existence and sensitivity of solutions of such problems, for both continuous and discrete cases, together with their implementation, are discussed. The authors also present basic numerical methods for solving Euler and Navier-Stokes equations, the discretization by finite elements or, for complex geometries, additionally the corresponding iterative solvers. The book describes also automatic differentiation programs, a very important technique in computational fluid dynamics. Besides different methods for the evaluation of the gradient of cost functions and constraints, the authors offer some C++ source codes which could be used within optimization algorithms. Some examples of shape optimization in two and three space dimensions for both inviscid and viscous turbulent flows at Mach numbers ranging from 0 to 20 close the book. This book will be very useful to applied mathematicians and engineers interested in the solution and implementation of optimization problems, and in the research and development areas involving realistic applications.