Shape optimization for suppressing coherent structure of two-dimensional open cavity flow

Abstract

This paper presents an optimal design obtained as a shape optimization problem in a domain with a singular point. For shape optimization, the eigenvalue in Snapshot Proper Orthogonal Decomposition (Snapshot POD) is defined as a cost function. The main problems are a Non-stationary Navier–Stokes problem and eigenvalue problem of Snapshot POD. An objective functional is described using Lagrange multipliers and finite element method. Twodimensional open cavity flow is adopted for an initial domain, where the domain includes a singular point. In this paper, two kinds of sensitivities assuming velocity vector in H1 and H2 are used. Using H1 gradient method for domain deformation, all triangles over a mesh are deformed as the cost function decreases. Finally, eigenvalues of Snapshot POD are compared in the initial and optimal domains.