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Improved Parabolization of the Euler Equations

Towne, Aaron and Colonius, Tim (2013) Improved Parabolization of the Euler Equations. In: 19th AIAA/CEAS Aeroacoustics Conference, 27-29 May 2013, Berlin, Germany.

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We present a new method for stability and modal analysis of shear flows and their acoustic radiation. The Euler equations are modified and solved as a spatial initial value problem in which initial perturbations are specified at the flow inlet and propagated downstream by integration of the equations. The modified equations, which we call one-way Euler equations, differ from the usual Euler equations in that they do not support upstream acoustic waves. It is necessary to remove these modes from the Euler operator because, if retained, they cause instability in the spatial marching procedure. These modes are removed using a two-step process. First, the upstream modes are partially decoupled from the downstream modes using a linear similarity transformation. Second, the error in the first step is eliminated using a convergent recursive filtering technique. A previous spatial marching method called the parabolized stability equations uses numerical damping to stabilize the march, but this has the unintended consequence of heavily damping the downstream acoustic waves. Therefore, the one-way Euler equation could be used to obtain improved accuracy over the parabolized stability equations as a low-order model for noise simulation of mixing layers and jets.

Item Type:Conference or Workshop Item (Paper)
Related URLs:
URLURL TypeDescription Paper Paper
Towne, Aaron0000-0002-7315-5375
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2013 by Aaron Towne and Tim Colonius. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Published Online: 24 May 2013. The authors gratefully acknowledge support from the Office of Naval Research under contract N0014-11-1-0753 with Dr. Brenda Henderson as technical monitor, and from NAVAIR under STTR contract N68335-11-C-0026 with Dr. John Spyropoulos as technical monitor. Additionally, the authors would like to thank Professor Thomas Hagstrom, Southern Methodist University and Professor Peter Schmid, École Polytechnique, for their helpful input on this work.
Funding AgencyGrant Number
Office of Naval Research (ONR)N0014-11-1-0753
Naval Air Systems Command (NAVAIR)N68335-11-C-0026
Subject Keywords:Aeroacoustics
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Other Numbering System NameOther Numbering System ID
AIAA Paper2013-2171
Record Number:CaltechAUTHORS:20190712-112322471
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97116
Deposited By: Melissa Ray
Deposited On:15 Jul 2019 20:51
Last Modified:16 Nov 2021 17:26

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