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Comparison Between Navier-Stokes and Thin-Layer Computations for Separated Supersonic FlowIn the numerical simulation of high Reynolds-number flow, one can frequently supply only enough grid points to resolve the viscous terms in a thin layer. As a consequence, a body-or stream-aligned coordinate system is frequently used and viscous terms in this direction are discarded. It is argued that these terms cannot be resolved and computational efficiency is gained by their neglect. Dropping the streamwise viscous terms in this manner has been termed the thin-layer approximation. The thin-layer concept is an old one, and similar viscous terms are dropped, for example, in parabolized Navier-Stokes schemes. However, such schemes also make additional assumptions so that the equations can be marched in space, and such a restriction is not usually imposed on a thin-layer model. The thin-layer approximation can be justified in much the same way as the boundary-layer approximation; it requires, therefore, a body-or stream-aligned coordinate and a high Reynolds number. Unlike the boundary-layer approximation, the same equations are used throughout, so there is no matching problem. Furthermore, the normal momentum equation is not simplified and the convection terms are not one-sided differenced for marching. Consequently, the thin-layer equations are numerically well behaved at separation and require no special treatment there. Nevertheless, the thin-layer approximation receives criticism. It has been suggested that the approximation is invalid at separation and, more recently, that it is inadequate for unsteady transonic flow. Although previous comparisons between the thin-layer and Navier-Stokes equations have been made, these comparisons have not been adequately documented.
Document ID
19990040816
Acquisition Source
Ames Research Center
Document Type
Reprint (Version printed in journal)
Authors
Degani, David
(National Academy of Sciences - National Research Council Moffett Field, CA United States)
Steger, Joseph L.
(Stanford Univ. Stanford, CA United States)
Date Acquired
August 19, 2013
Publication Date
November 1, 1983
Publication Information
Publication: AIAA Journal
Publisher: American Institute of Aeronautics and Astronautics
Volume: 21
Issue: 11
Subject Category
Composite Materials
Distribution Limits
Public
Copyright
Other

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