Embedded WENO: A design strategy to improve existing WENO schemes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:330

Article

van Lith, Bart S.¹  Boonkkamp, Jan H. M. ten Thije¹  IJzerman, Wilbert L.^1,2 

[1] Eindhoven Univ Technol, Dept Math & Comp Sci, POB 513, NL-5600 MB Eindhoven, Netherlands

[2] Philips Lighting, High Tech Campus 44, NL-5656 AE Eindhoven, Netherlands

关键词: Essentially non-oscillatory;    WENO;    High-resolution scheme;    Hyperbolic conservation laws;    Nonlinear interpolation;    Spectral analysis;   

DOI  :  10.1016/j.jcp.2016.11.026

来源: Elsevier

【 摘 要 】

Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free