A New Hybrid WENO Scheme with the High-Frequency Region for Hyperbolic Conservation Laws

doi:10.1007/s42967-021-00153-2

Abstract

Abstract: In this paper, a new kind of hybrid method based on the weighted essentially non-oscillatory (WENO) type reconstruction is proposed to solve hyperbolic conservation laws. Comparing the WENO schemes with/without hybridization, the hybrid one can resolve more details in the region containing multi-scale structures and achieve higher resolution in the smooth region; meanwhile, the essentially oscillation-free solution could also be obtained. By adapting the original smoothness indicator in the WENO reconstruction, the stencil is distinguished into three types: smooth, non-smooth, and high-frequency region. In the smooth region, the linear reconstruction is used and the non-smooth region with the WENO reconstruction. In the high-frequency region, the mixed scheme of the linear and WENO schemes is adopted with the smoothness amplification factor, which could capture high-frequency wave efficiently. Spectral analysis and numerous examples are presented to demonstrate the robustness and performance of the hybrid scheme for hyperbolic conservation laws.

Key words: Hybrid schemes, WENO reconstruction, Smoothness indicator, Finite difference method

CLC Number:

65M06
35L65

Yifei Wan, Yinhua Xia. A New Hybrid WENO Scheme with the High-Frequency Region for Hyperbolic Conservation Laws[J]. Communications on Applied Mathematics and Computation, 2023, 5(1): 199-234.

TrendMD

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