An improved RBF-WENO scheme for hyperbolic conservation laws

Yang Sun and Ai-Qi Han

Applied Mathematics and Computation, 2025, vol. 501, issue C

Abstract: In this paper, a novel fifth-order weighted essentially non-oscillatory (WENO) scheme by using radial basis function (RBF) is proposed to solve hyperbolic conservation laws. The key idea is to choose multi-quadric (MQ) RBF and trigonometric function to construct numerical flux and smoothness indicator respectively. First, we modify the RBF interpolation making it into the WENO reconstruction framework along with representing it by a perturbation of polynomial. The explicit form of disturbance term on each stencil is given. Through selecting the appropriate shape parameters of MQ RBF, the relevant WENO scheme achieves sixth-order accuracy than other well-known fifth-order WENO schemes under some conditions. Moreover, some differential operators based on trigonometric function space are employed to obtain new smoothness indicators that efficiently evaluates the sharp change of gradient on the candidate stencil. To highlight the effectiveness of the proposed WENO scheme, this new scheme is applied to several one and two-dimensional hyperbolic test problems, and compared with the existing schemes such as WENO-JS, WENO-M and WENO-Z. The numerical results show higher accuracy can be achieved in the smooth regions of the solutions, and no non-physical oscillations occur near the discontinuities, which verifies the higher resolution property and the better discontinuity-capturing ability of the improved scheme.

Keywords: WENO scheme; Smoothness indicator; Radial basis function; Shape parameter; Trigonometric function; Hyperbolic conservation laws (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300325001985
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:501:y:2025:i:c:s0096300325001985

DOI: 10.1016/j.amc.2025.129472

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().