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Stability analysis and aerodynamic design optimization of euler equations using variational methods
Author(s) -
Ibrahim Adem H.,
Tiwari Surendra N.,
Smith Robert E.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990420)44:11<1709::aid-nme567>3.0.co;2-o
Subject(s) - euler equations , inviscid flow , sensitivity (control systems) , mathematics , euler method , simultaneous equations , stability (learning theory) , boundary value problem , state variable , differential equation , mathematical analysis , computer science , physics , classical mechanics , engineering , electronic engineering , machine learning , thermodynamics
The one‐ and two‐dimensional inviscid Euler equations are formulated in an integro‐differential form for shape design sensitivity analysis and optimization. The principal tool employed to derive the performance derivative sensitivity equations is the variational method, which is a continuous alternative to the discrete sensitivity analysis. Along with the sensitivity equations, the co‐state equations and their boundary conditions are derived. Thereafter, based on the modal analysis of Von Neumann theory, the stability limits of the co‐state equations are investigated. The stability characteristics of the co‐state equations are compared with those of the Euler equations. Finally, using the criteria from the stability analysis of the state and co‐state equations, some results of shape design optimization and sensitivity analysis for both quasi one‐ and two‐dimensional Euler equations are presented. Copyright © 1999 John Wiley & Sons, Ltd.