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A flux‐based modified method of characteristics
Author(s) -
Roache Patrick J.
Publication year - 1992
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.1650151103
Subject(s) - courant–friedrichs–lewy condition , flux limiter , mathematics , integer (computer science) , flux (metallurgy) , constant (computer programming) , limiter , stability (learning theory) , closure (psychology) , integer programming , mathematical optimization , algorithm , mathematical analysis , computer science , market economy , telecommunications , materials science , machine learning , discretization , economics , metallurgy , programming language
A flux‐based modified method of characteristics (MMOC) methodology in 1D is described which has the following properties: unconditional stability (though explicit), exact answers for integer CFL (Courant) numbers, completely conservative (locally and globally) and able to utilize various flux limiters and various characteristic‐ (trajectory‐) tracking algorithms. The use of characteristics based on cell‐wise constant characteristic velocities results in considerable code simplification, and Van Leer's MUSCL is an accurate and cost‐effective flux limiter. For CFL ≥1 the flux limiter is applied only to the non‐integer part of CFL , whereas the integer part is exact for constant velocities; therefore accuracy improves with larger CFL . It is not a cheap algorithm, although explicit, because the operation count per time step increases with the integer part of CFL , but it is much more accurate than the commonly used implicit upstream differencing. This flux‐based MMOC method is well suited for groundwater flow calculations in which large local Courant numbers arise owing to grid clustering.