Review of summation-by-parts schemes for initial-boundary-value problems

By Magnus Svärd, Jan Nordström. Journal of Computational Physics, 2013

497 citations recorded by the source corpus.

High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback has been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-by-parts operators and weak boundary conditions during the last 20 years has removed this drawback and now reached a mature state. It is now possible to construct stable and high order accurate multi-block finite difference schemes in a systematic building-block-like manner. In this paper we will review this development, point out the main contributions and speculate about the next lines of research in this area.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/cadb1df8d1657b6dc21d963790ab152fed3abcc6

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In Computational Mechanics

1. Hugo Gagnon
2. David W. Zingg
3. Joaquim R. Martins
4. O. Chernukhin
5. Xiaocong Han
6. Gaetan K. W. Kenway

In Electrical and Electronic Engineering

1. Hugo Gagnon
2. David W. Zingg

Citations in the corpus

• Two-Level Free-Form and Axial Deformation for Exploratory Aerodynamic Shape Optimization (2015, methodology): “The spatial derivatives are discretized with second-order accurate finite-difference summation-by-parts operators, while simultaneous approximation terms enforce boundary conditions and couple blocks, requiring only C0 continuity between matching grid lines at interfaces [50, 51].”