Three-Dimensional Shape Optimization in Viscous Incompressible Flows
Abstract
The integral equation constrained optimization approach to finding three-dimensional minimum-drag shapes for bodies translating in viscous incompressible fluid has been developed. The approach relies on the theory of generalized analytic functions for obtaining efficient integral equations for 3D boundary-value problems with linear partial differential equations (PDEs). The theory has been developed in application to 3D Stokes and Oseen flows, two-phase Stokes flows and 3D magnetohydrodynamic (MHD) flows governed by linearized MHD equations. In shape optimization problems, the suggested approach replaces 3D boundary-value problems with governing PDEs by corresponding boundary integral equations. Minimum-drag shapes, represented in finite function series form, are then found by the adjoint equation-based method with a gradient-based algorithm, in which the gradient for shape series coefficients is determined analytically. Compared to PDE constrained optimization coupled with the finite element method (FEM), the approach reduces dimensionality of the flow problems, solves the issue with region truncation in exterior problems, finds minimum-drag shapes in semi-analytical form, and has fast convergence.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 2011
- Accession Number
- ADA565963
Entities
People
- Michael Zabarankin
Organizations
- Stevens Institute of Technology