Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates

JOURNAL OF COMPUTATIONAL PHYSICS

卷:392

Article

Fernandez, David C. Del Rey^1,2  Crean, Jared³  Carpenter, Mark H.²  Hicken, Jason E.³ 

[1] Natl Inst Aerosp, Hampton, VA USA

[2] NASA, Langley Res Ctr, Computat AeroSci Branch, Hampton, VA 23665 USA

[3] Rensselaer Polytech Inst, Dept Mech Aerosp & Nucl Engn, Troy, NY USA

关键词: Nonlinear entropy stability;    Summation-by-parts;    Simultaneous approximation terms;    High-order discretizations;    General elements and curved elements;    Unstructured grid;   

DOI  :  10.1016/j.jcp.2019.04.029

来源: Elsevier

【 摘 要 】

The entropy conservative/stable staggered grid tensor-product algorithm of Parsani et al. [1] is extended to multidimensional SBP discretizations. The required SBP preserving interpolation operators are proven to exist under mild restrictions and the resulting algorithm is proven to be entropy conservative/stable as well as elementwise conservative. For 2-dimensional simplex elements, the staggered grid algorithm is shown to be more accurate and have a larger maximum time step restriction as compared to the collocated algorithm. The staggered algorithm significantly reduces the number of (computationally expensive) two-point flux evaluations, which is potentially important for both explicit and implicit time-marching schemes. Furthermore, the staggered algorithm requires fewer degrees of freedom for comparable accuracy, which has favorable implications for implicit time-marching schemes. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free