A second-order iterative implicit-explicit hybrid scheme for hyperbolic systems of conservation laws

Wenlong Dai, Paul R. Woodward

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

An iterative implicit-explicit hybrid scheme is proposed for hyperbolic systems of conservation laws. Each wave in a system may be implicitly, or explicitly, or partially implicitly and partially explicitly treated depending on its associated Courant number in each numerical cell, and the scheme is able to smoothly switch between implicit and explicit calculations. The scheme is of Godunov-type in both explicit and implicit regimes, is in a strict conservation form, and is accurate to second-order in both space and time for all Courant numbers. The computer code for the scheme is easy to vectorize. Multicolors proposed in this paper may reduce the number of iterations required to reach a converged solution by several orders for a large time step. The feature of the scheme is shown through numerical examples.

Original languageEnglish (US)
Pages (from-to)181-196
Number of pages16
JournalJournal of Computational Physics
Volume128
Issue number1
DOIs
StatePublished - Oct 1 1996

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation under Grant NSF-ASC-9309829, the Department of Energy under Grant DEF602-87ER25035, the Laboratory for Computational Science and Engineering, and the Minnesota Supercomputer Institute.

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