Extended skew-symmetric form for summation-by-parts operators and varying Jacobians

JOURNAL OF COMPUTATIONAL PHYSICS

卷:342

Article

Ranocha, Hendrik¹  Oeffner, Philipp¹  Sonar, Thomas¹ 

[1] TU Braunschweig, Inst Computat Math, Pockelsstr 14, D-38106 Braunschweig, Germany

关键词: Hyperbolic conservation laws;    High order methods;    Summation-by-parts;    Skew-symmetric form;    Correction procedure via reconstruction;    Entropy stability;   

DOI  :  10.1016/j.jcp.2017.04.044

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free