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A numerical method for inverse design based on the inverse Euler equations
Author(s) -
Scascighini A.,
Troxler A.,
Jeltsch R.
Publication year - 2003
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.439
Subject(s) - euler equations , euler's formula , inverse , discretization , backward euler method , euler method , mathematics , semi implicit euler method , mathematical analysis , inverse problem , numerical analysis , geometry
We present a numerical method for the inverse shape design of internal flows based on the inverse Euler equations (Keller JJ, Physics of Fluids 1999; 11 and Zeitschrift für Angewandte Mathematik und Physik 1998; 49 ). We describe an efficient numerical method based on a finite difference discretization and on a Newton–Krylov solver. After showing that the three‐dimensional (3D) inverse Euler equations hold only for complex lamellar flows, we extend the basic axis‐symmetric flow model to handle viscous effects by means of a distributed loss model and to handle quasi‐3D effects by deriving a quasi‐3D formulation of the inverse Euler equations from the passage averaged 3D Euler equations. The coupling of the 2D inverse Euler equations with an integral boundary layer method is presented too. Copyright © 2003 John Wiley & Sons, Ltd.