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. Two-dimensional 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.

Keywords

• shape optimization problem
• snapshot proper orthogonal decomposition
• two-dimensional open cavity