A note on non‐negativity correction for a multimoment finite‐volume transport model with WENO limiter. (5th December 2019)

• Record Type: Journal Article
• Authors: Li, Xingliang; Shen, Xueshun; Chen, Chungang; Tang, Jie; Xiao, Feng
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 146:Number 726(2020)
• Page Start: 546
• Page End: 556
• Publication Date: 2019-12-05
• Subjects: cubed sphere -- multimoment method -- non‐negativity scheme -- transport model -- WENO method; Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.3675
• Languages: English
• ISSNs: 0035-9009

Abstract

Abstract: An oscillation‐less multimoment global transport model was proposed by Tang et al . in 2018 by introducing a slope limiter based on the weighted essentially non‐oscillatory (WENO) concept. The spurious oscillations around the discontinuities and strong gradients can be effectively removed and the model preserves the fourth‐order accuracy in spherical geometry for smooth solutions. However, the WENO limiter does not strictly guarantee the non‐negativity of numerical solution and the resulting model will violate the physical principle due to the existence of the nonphysical negative undershoots. As the numerical fluxes, which determine the time tendency of the volume‐integrated average, are evaluated by the point values (PVs) defined along the cell boundaries in the multimoment finite‐volume schemes, the non‐negativity preserving model can be accomplished by modifying those PVs to implement the corrections on the numerical fluxes proposed in the positive definite flux‐corrected transport (FCT) method by Smolarkiewicz in 1989. In this study, a non‐negativity correction algorithm is proposed for a global transport model using the MM‐FVM_WENO scheme and verified by simulating the widely used benchmark tests. Abstract : Relative maximum and minimum errors of deformational flow test by MM‐FVM_WENO_FC scheme