Numerical Shape Optimization of an Isothermal Compressible Navier–Stokes Flow

We consider numerical shape optimization of a compressible isothermal fluid model. The constrained system involves regularized compressible isothermal Navier–Stokes equations. The distributed and boundary type of shape gradients for objective functions (such as inverse problem, and energy dissipation power type) are derived via the adjoint method. The regularized Navier–Stokes equations are discretized with mixed finite element method and solved by the Leray-Schauder fixed point iterative scheme. Numerical results are presented to illustrate the effectiveness of the optimization algorithm proposed.