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Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions
Computational Aerosciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA.
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
Department of Mathematics, North Carolina A&T State University, Greensboro, NC 27411, USA.
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2013 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 234, 353-375 p.Article in journal (Refereed) Published
Abstract [en]

The Lax-Wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities. The discrete operator, however, need not be derived from the divergence form of the continuous equations. Indeed, conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm skew-symmetric summation-by-parts (SBP) spatial operator, yield discrete operators that are conservative. Furthermore, split-form, discretely conservation operators can be derived for periodic or finite-domain SBP spatial operators of any order. Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and are supplied in an accompanying text file.

Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 234, 353-375 p.
Keyword [en]
High-order finite-difference methods; Lax-Wendroff; Conservation; Skew-symmetric; Numerical stability
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-84553DOI: 10.1016/ 000311644900019OAI: diva2:560216

funding agencies|NASA|NNX09AV08A|Army Research Laboratory|W911NF-06-R-006|

Available from: 2012-10-12 Created: 2012-10-12 Last updated: 2013-08-30

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