NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
Positivity-preserving numerical schemes for multidimensional advectionThis report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.
Document ID
19930017902
Document Type
Technical Memorandum (TM)
Authors
Leonard, B. P. (NASA Lewis Research Center Cleveland, OH, United States)
Macvean, M. K. (Meteorological Office Bracknell, United Kingdom)
Lock, A. P. (Meteorological Office Bracknell, United Kingdom)
Date Acquired
September 6, 2013
Publication Date
March 1, 1993
Subject Category
FLUID MECHANICS AND HEAT TRANSFER
Report/Patent Number
NASA-TM-106055
ICOMP-93-05
E-7656
NAS 1.15:106055
Funding Number(s)
CONTRACT_GRANT: NCC3-233
PROJECT: RTOP 505-90-5K
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

Available Downloads

NameType 19930017902.pdf STI