Optimal shape design for the time‐dependent Navier–Stokes flow

Abstract

SUMMARYThis paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients for time-dependent cost functionals by using the state derivative and its associated adjoint state. Finally, we apply a gradienttype algorithm to our problem, and numerical examples show that our theory is useful for practical purposes and the proposed algorithm is feasible in low Reynolds number flows.

Adjoint shape design sensitivity analysis of molecular dynamics for lattice structures using GLE impedance forces

“…For transient dynamic problems with large deformation elastic-plastic materials, an analytical DSA method (Cho and Choi 2000) is developed in updated Lagrangian formulation. Gao et al (2008) performed shape optimization for timedependent Navier-Stokes flows. They used a Piola transformation to bypass the divergence-free condition for shape DSA.…”

Multiscale adjoint design sensitivity analysis of atomistic-continuum dynamic systems using bridging scale decomposition

“…Totorelli et al (1991) developed an adjoint DSA method for nonlinear dynamic thermo-elastic systems. Gao et al (2008) performed shape optimization for time-dependent Navier-Stokes flows. They used the Piola transformation to bypass the divergence-free condition for the shape DSA.…”