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Accuracy and stability of semi-implicit finite difference advection schemes

✍ Scribed by Gjesdal, Thor ;Teigland, Rune

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 134 KB
Volume: 14
Category: Article
ISSN: 1069-8299
DOI: 10.1002/(sici)1099-0887(199807)14:7<647::aid-cnm178>3.0.co;2-z

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✦ Synopsis

This paper discusses implementation strategies for second-order ®nite dierence discretizations of advection. Purely explicit and implicit methods both have disadvantages, and we consider semi-implicit schemes in which the ¯ux is split into a primary implicit part and a secondary explicit correction. Onedimensional scalar advection is used as a model problem to analyse the leading order error terms and the stability of the schemes. Some of the splittings turn out to be unconditionally stable, but accuracy or monotonicity may deteriorate for large time steps.

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