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Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference schemeA fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.
Document ID
19890005423
Document Type
Technical Memorandum (TM)
Authors
Leonard, B. P. (NASA Lewis Research Center Cleveland, OH, United States)
Date Acquired
September 5, 2013
Publication Date
September 1, 1988
Subject Category
NUMERICAL ANALYSIS
Report/Patent Number
NASA-TM-100916
E-4169
NAS 1.15:100916
ICOMP-88-11
Funding Number(s)
PROJECT: RTOP 505-62-21
CONTRACT_GRANT: NASA ORDER C-99066-G
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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