New limiter regions for multidimensional flows

Woodfield, J., Weller, H. ORCID: https://orcid.org/0000-0003-4553-7082 and Cotter, C. J. (2024) New limiter regions for multidimensional flows. Journal of Computational Physics, 515. 113286. ISSN 0021-9991 doi: 10.1016/j.jcp.2024.113286

Abstract/Summary

Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is commonly employed to suppress nonphysical oscillations. However, the application of such limiters can reduce accuracy. It is important to identify the weakest set of sufficient conditions required on the limiter as to allow the development of successful numerical algorithms. The main goal of this paper is to identify new less restrictive sufficient conditions for flux form in-compressible advection to remain monotonic. We identify additional necessary conditions for incompressible flux form advection to be monotonic, demonstrating that the Spekreijse limiter region is not sufficient for incompressible flux form advection to remain monotonic. Then a convex combination argument is used to derive new sufficient conditions that are less restrictive than the Sweby region for a discrete maximum principle. This allows the introduction of two new more general limiter regions suitable for flux form incompressible advection.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/117552
Identification Number/DOI	10.1016/j.jcp.2024.113286
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Elsevier
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