Abstract
We consider the energy dissipation minimization constrained by steady Navier–Stokes flows. The nonlinearity of the Navier–Stokes equation causes its numerical solver computationally expensive and thus leads to inefficiency of shape optimization algorithms. We propose a new efficient shape gradient algorithm of distributed type by using a two-grid solver for the Navier–Stokes equation. Asymptotically optimal convergence rate is shown for mixed finite-element approximation of the two-grid distributed shape gradient. Moreover, a Uzawa iterative scheme for Stokes-type systems is adopted in the two-grid solver and a new scalar-type shape gradient flow is proposed to improve significantly the computational efficiency especially for 3D. Numerical experiments are presented to verify theoretical analysis and show effectiveness of two-grid shape gradient optimization algorithms.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Computer Methods in Applied Mechanics and Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
