In this article we intend to find the optimal shape of a nozzle respecting to some given target flow fields including viscosity effect. Via an approach based on measure theory which is not an iterative method and need not to any initial guess, each shape optimization problems are solved and consequently each geometry of the nozzle corresponding to prescribed flow fields is determined. Analyzing several case studies make us to confident on the use of the presented approach, because the obtained results give entirely the same as what we expect physically.
Navier-Stokes equations Optimal shape design (OSD) Optimal control Measure theory Linear programming problem
This is a preview of subscription content, log in to check access.
Farhadinia, B., Farahi, M.H.: Optimal shape design of an almost straight Nozzle. Int. J. Appl. Math. 17(3), 319–333 (2005)
Gunzburger, M., Kim, H.: Existence of an optimal solution of a shape control problem for the stationary Navier-Stokes equations. SIAM J. Control Optim. 36(3), 895–909 (1998)
Gunzburger, M., Manservisi, S.: Flow matching by shape design for the Navier-Stokes system. Int. Ser. Numer. Math. 139, 279–289 (2001)