Shape Optimization Governed by the Euler Equations Using an Adjoint Method

Abstract

In this paper we discuss a numerical approach for the treatment of optimal shape problems governed by the Euler equations. In particular, we focus on flows with embedded shocks. We consider a very simple problem: the design of a quasi-one-dimensional Laval nozzle. We introduce a cost function and a set of Lagrange multipliers to achieve the minimum. The nature of the resulting costate equations is discussed. A theoretical difficulty that arises for cases with embedded shocks is pointed out and solved. Finally, some results are given to illustrate the effectiveness of the method.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1993
Accession Number
ADA274347

Entities

People

  • Angelo Iollo
  • Manuel D. Salas
  • Shlomo Taasan

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Computers
  • Curvature
  • Discontinuities
  • Engineering
  • Equations
  • Euler Equations
  • Flow
  • Flow Fields
  • Fluid Dynamics
  • Geometry
  • Nozzles
  • Pressure Distribution
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.