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A systematic method to enforce conservativity on semi‐Lagrangian schemes
Author(s) -
Cameron Alexandre
Publication year - 2018
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.4675
Subject(s) - advection , mathematics , lagrangian , property (philosophy) , stability (learning theory) , scheme (mathematics) , instability , range (aeronautics) , mathematical optimization , mathematical analysis , computer science , mechanics , machine learning , composite material , thermodynamics , philosophy , physics , materials science , epistemology
Summary Semi‐Lagrangian schemes have proven to be very efficient in modeling advection problems. However, most semi‐Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a semi‐Lagrangian advection scheme. This method is shown to generate conservative schemes with the same linear stability range and the same order of accuracy as the initial advection scheme from which they are derived. We used a criterion based on the column‐balance property of the schemes to assess their conservativity property. We introduce an unsplit geometrical reconstruction that enforces conservativity. We show that this approach can be used with large Courant‐Friedrichs‐Lewy numbers and third‐order schemes. We give a physical application in the case of the Rayleigh‐Taylor instability.