A third-order weighted nonlinear scheme for hyperbolic conservation laws with inverse Lax-Wendroff boundary treatment

Tianchu Hao, Yaming Chen, Lingyan Tang and Songhe Song

Applied Mathematics and Computation, 2023, vol. 441, issue C

Abstract: Cartesian grids are often used in applications due to the simplicity of grid generation and the efficiency of discretization algorithms. However, for problems with curved boundaries, grid points are often away from the boundaries, leading to the issue of imposing boundary conditions. Recently, it was shown that the inverse Lax-Wendroff (ILW) boundary treatment is very useful for addressing this issue. While most of the investigations focus on the WENO schemes for hyperbolic conservation laws, we present in this paper a new third-order weighted nonlinear scheme, which is based on the framework of weighted compact nonlinear schemes. We show that the scheme is applicable directly on Cartesian grids by using the ILW boundary treatment. To demonstrate the linear stability of the scheme, both the method of eigenvalue analysis and the Gustafsson-Kreiss-Sundström (GKS) theory are employed and analyzed in details. Some numerical tests are also performed to show the accuracy and validity of the proposed method.

Keywords: Weighted nonlinear scheme; Cartesian grid; ILW boundary treatment; Eigenvalue analysis; GKS theory (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300322007652
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:441:y:2023:i:c:s0096300322007652

DOI: 10.1016/j.amc.2022.127697

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 ().