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arXiv · 1511.08408

Extended Skew-Symmetric Form for Summation-by-Parts Operators and Varying Jacobians

Hendrik Ranocha·Philipp Öffner·Thomas Sonar
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Abstract

A generalised analytical notion of summation-by-parts (SBP) methods is proposed, extending the concept of SBP operators in the correction procedure via reconstruction (CPR), a framework of high-order methods for conservation laws. For the first time, SBP operators with dense norms and not including boundary points are used to get an entropy stable split-form of Burgers' equation. Moreover, overcoming limitations of the finite difference framework, stability for curvilinear grids and dense norms is obtained for SBP CPR methods by using a suitable way to compute the Jacobian.

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Hendrik Ranocha, Philipp Öffner, Thomas Sonar. 2015-11-26. Extended Skew-Symmetric Form for Summation-by-Parts Operators and Varying Jacobians. https://doi.org/10.1016/j.jcp.2017.04.044

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