TY - GEN
T1 - Lst and the eigenfunction expansion method for linearized navier-stokes equations – a summary
AU - Tumin, Anatoli
N1 - Funding Information:
The author thanks Dr. A. Fedorov and Mr. K. Luna for helpful discussions of the manuscript and fruitful ideas for the method presentation. The work was supported by ONR Grant N00014-17-1-2343 monitored by Dr. E. Marineau.
Publisher Copyright:
© 2020 American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
PY - 2020
Y1 - 2020
N2 - The eigenfunction system corresponding to the Linear Stability Theory (LST) equations is discussed from the perspective of a basis for the eigenfunction expansion method for the Linearized Navier-Stokes Equations (LNSE). The method may lead to an infinite system of coupled ODEs or integro-differential equations. An approximation/truncation is needed to solve an initial boundary-value problem for linearized Navier-Stokes equations using this method. Examples include coupling of modes due to weakly nonparallel flow effect, scattering of an acoustic wave on a localized roughness, initial-value problem for perturbations in boundary layers, distributed forcing due to impinging particulates or thermal noise, and an actuator located on a wall. The BiGlobal/TriGlobal system of eigenfunctions can also be used for solving the Linearized Navier-Stokes equations in other complex flows along the same lines of the eigenfunction expansion method.
AB - The eigenfunction system corresponding to the Linear Stability Theory (LST) equations is discussed from the perspective of a basis for the eigenfunction expansion method for the Linearized Navier-Stokes Equations (LNSE). The method may lead to an infinite system of coupled ODEs or integro-differential equations. An approximation/truncation is needed to solve an initial boundary-value problem for linearized Navier-Stokes equations using this method. Examples include coupling of modes due to weakly nonparallel flow effect, scattering of an acoustic wave on a localized roughness, initial-value problem for perturbations in boundary layers, distributed forcing due to impinging particulates or thermal noise, and an actuator located on a wall. The BiGlobal/TriGlobal system of eigenfunctions can also be used for solving the Linearized Navier-Stokes equations in other complex flows along the same lines of the eigenfunction expansion method.
UR - http://www.scopus.com/inward/record.url?scp=85091739852&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85091739852&partnerID=8YFLogxK
U2 - 10.2514/6.2020-0105
DO - 10.2514/6.2020-0105
M3 - Conference contribution
AN - SCOPUS:85091739852
SN - 9781624105951
T3 - AIAA Scitech 2020 Forum
SP - 1
EP - 17
BT - AIAA Scitech 2020 Forum
PB - American Institute of Aeronautics and Astronautics Inc, AIAA
T2 - AIAA Scitech Forum, 2020
Y2 - 6 January 2020 through 10 January 2020
ER -