WENO finite volume scheme using subcell strategy on rectangular meshes

Li Li Chen and Cong Huang

Applied Mathematics and Computation, 2024, vol. 471, issue C

Abstract: WENO scheme is popular for solving hyperbolic conservation laws. However for the traditional WENO schemes, they often increase the order of accuracy by enlarging the stencil, thus lack the compactness and do not obtain the highest resolution and efficiency. In order to overcome this problem, we consider to improve the traditional WENO scheme by using subcell strategy, which basic idea is that: first, in order to obtain higher resolution, each control volume is divided into some subcells further; second, in order to save the computational cost, the WENO reconstruction is still implemented on the control volume; finally, in order to keep the compactness, the whole subcells in control volume and whole or part of subcells in neighbor ones are used to construct the final WENO reconstruction. To the best of our knowledge, the corresponding research is still limited. In this paper, we first propose the framework of WENO scheme with subcell strategy, in which various WENO techniques can be used for the spatial reconstruction in theory; then two traditional WENO schemes, i.e., XWENO (X=DK and AO), are selected for the improvement. The resulted XWENO-SC (X=DK and AO) schemes not only inherit the high order of accuracy and ENO property of original WENO schemes, but also show their significant advantages in the compactness, resolution and efficiency.

Keywords: WENO scheme; Subcell strategy; Hyperbolic conservation laws; High resolution and efficiency; Compactness (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:471:y:2024:i:c:s0096300324000791

DOI: 10.1016/j.amc.2024.128607

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