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Methods for extending high‐resolution schemes to non‐linear systems of hyperbolic conservation laws
Author(s) -
Rider William J.
Publication year - 1993
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.1650171004
Subject(s) - conservation law , extension (predicate logic) , mathematics , scalar (mathematics) , polygon mesh , mathematical optimization , computer science , mathematical analysis , geometry , programming language
In extending high‐resolution methods from the scalar case to systems of equations there are a number of options available. These options include working with either conservative or primitive variables, characteristic decomposition, two‐step methods, or component‐wise extension. In this paper, several of these options are presented and compared in terms of economy and solution accuracy. The characteristic extension with either conservative or primitive variables produces excellent results with all the problems solved. Using primitive variables, the two‐step formulation produces high‐quality results in a more economical manner. This method can also be extended to multiple dimensions without resorting to dimensional splitting. Proper selection of limiters is also important in non‐characteristic extension to systems.