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Local maximum principle satisfying high‐order non‐oscillatory schemes
Author(s) -
Dubey Ritesh Kumar,
Biswas Biswarup,
Gupta Vikas
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4202
Subject(s) - maxima and minima , mathematics , clipping (morphology) , maximum principle , stability (learning theory) , work (physics) , order (exchange) , algorithm , mathematical optimization , mathematical analysis , computer science , physics , optimal control , thermodynamics , philosophy , linguistics , finance , machine learning , economics
Summary The main contribution of this work is to classify the solution region including data extrema for which high‐order non‐oscillatory approximation can be achieved. It is performed in the framework of local maximum principle (LMP) and non‐conservative formulation. The representative uniformly second‐order accurate schemes are converted in to their non‐conservative form using the ratio of consecutive gradients. Using the local maximum principle, these non‐conservative schemes are analyzed for their non‐linear LMP/total variation diminishing stability bounds which classify the solution region where high‐order accuracy can be achieved. Based on the bounds, second‐order accurate hybrid numerical schemes are constructed using a shock detector. The presented numerical results show that these hybrid schemes preserve high accuracy at non‐sonic extrema without exhibiting any induced local oscillations or clipping error. Copyright © 2015 John Wiley & Sons, Ltd.