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Giddings, Thomas Edward.

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Theoretical and numerical study of the propagation of weak shock waves in weakly heterogeneous fluid media.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theoretical and numerical study of the propagation of weak shock waves in weakly heterogeneous fluid media./
Author:	Giddings, Thomas Edward.
Description:	134 p.
Notes:	Source: Dissertation Abstracts International, Volume: 61-01, Section: B, page: 0309.
Contained By:	Dissertation Abstracts International61-01B.
Subject:	Physics, Acoustics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9958515
ISBN:	9780599618169

Theoretical and numerical study of the propagation of weak shock waves in weakly heterogeneous fluid media.
Giddings, Thomas Edward.

Theoretical and numerical study of the propagation of weak shock waves in weakly heterogeneous fluid media. - 134 p.

Source: Dissertation Abstracts International, Volume: 61-01, Section: B, page: 0309.

Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 1999.

A nonlinear model which describes the interaction of weak shock waves with heterogeneities in fluid media is derived. The model is an extension of the transonic small-disturbance (TSD) equations, with additional terms to account for slight variations in the heterogeneous media. The particular problem of a weak shock wave propagating through the turbulent atmospheric boundary layer is addressed. It is shown that the various linear theories necessarily fail to explain the observed behavior in this instance; but, the nonlinear theory, derived herein, is uniformly valid and accounts for all observed behavior. Various deterministic examples of interaction phenomena demonstrate good agreement with available experimental observations.

ISBN: 9780599618169Subjects--Topical Terms:

1019086
Physics, Acoustics.

Theoretical and numerical study of the propagation of weak shock waves in weakly heterogeneous fluid media.
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100 1 $a Giddings, Thomas Edward. $3 1912407
245 1 0 $a Theoretical and numerical study of the propagation of weak shock waves in weakly heterogeneous fluid media.
300 $a 134 p.
500 $a Source: Dissertation Abstracts International, Volume: 61-01, Section: B, page: 0309.
500 $a Adviser: Jacob Fish.
502 $a Thesis (Ph.D.)--Rensselaer Polytechnic Institute, 1999.
520 $a A nonlinear model which describes the interaction of weak shock waves with heterogeneities in fluid media is derived. The model is an extension of the transonic small-disturbance (TSD) equations, with additional terms to account for slight variations in the heterogeneous media. The particular problem of a weak shock wave propagating through the turbulent atmospheric boundary layer is addressed. It is shown that the various linear theories necessarily fail to explain the observed behavior in this instance; but, the nonlinear theory, derived herein, is uniformly valid and accounts for all observed behavior. Various deterministic examples of interaction phenomena demonstrate good agreement with available experimental observations.
520 $a A stabilized finite element formulation for the transonic small-disturbance system of equations is then developed and used to solve a variety of problems in transonic aerodynamics. An adaptive mesh refinement technique and a common discontinuity capturing operator are used to resolve regions with large gradients in the velocity field. The scheme works well in both subsonic and supersonic flow regimes, and it captures shocks naturally. Agreement with available experimental observations and theoretical approximations is very good.
520 $a Finally, a two-level, linear algebraic solver for stabilized finite element formulations is developed. The algebraic systems are generally asymmetric (non-symmetric) and positive definite. Based on the analysis of a representative smoother, the parent space is divided into oscillatory and smooth subspaces according to the eigenvectors of the associated normal system. Using an aggregation technique, a restriction/prolongation operator is constructed for linear elements. Various numerical examples, on both structured and unstructured meshes, are performed using the two-level cycle as the basis for a preconditioner. The stabilized finite element formulation for the transonic small-disturbance system and various model problems are used to verify the multi-level methodology.
590 $a School code: 0185.
650 4 $a Physics, Acoustics. $3 1019086
650 4 $a Engineering, Mechanical. $3 783786
650 4 $a Computer Science. $3 626642
690 $a 0986
690 $a 0548
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710 2 0 $a Rensselaer Polytechnic Institute. $3 1019062
773 0 $t Dissertation Abstracts International $g 61-01B.
790 1 0 $a Fish, Jacob, $e advisor
790 $a 0185
791 $a Ph.D.
792 $a 1999
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9958515