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Smoothing and the second lawThe technique of obtaining second-order oscillation-free total -variation-diminishing (TVD), scalar difference schemes by adding a limited diffusive flux ('smoothing') to a second-order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell-by-cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second-order spatial accuracy was found to have extremely restrictive time-step limitation. Switching to an implicit scheme removed the time-step limitation.
Document ID
19880050132
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Merriam, Marshal L.
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
August 13, 2013
Publication Date
October 1, 1987
Publication Information
Publication: Computer Methods in Applied Mechanics and Engineering
Volume: 64
ISSN: 0045-7825
Subject Category
Numerical Analysis
Accession Number
88A37359
Distribution Limits
Public
Copyright
Other

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