Positivity‐preserving transport with local and global mass conservation on Yin–Yang grids

Abstract

This study proposed a new mass conservative constraint algorithm on Yin–Yang grids with positivity‐preserving property. The proposed method naturally achieves local and global mass conservations by sharing the flux on a common interface of the donor and receptor cells in both Yin and Yang component grids. A flux correction method is developed with a positive‐definite limiter to enforce positivity‐preserving transport across the common interface. Despite the additional constraints for numerical positivity and mass conservation, no significant degradation is found in numerical accuracy and computational efficiency. The computation of flux is limited entirely on the structured grid framework, even though irregular receptor cells are introduced on the Yin–Yang grid. The proposed scheme employs the finite‐volume method coupled with a three‐stage Runge–Kutta scheme and flux limiter to solve the flux‐form transport equation. The numerical performance of the model is validated with a series of idealized tests of scalar advection. Numerical results demonstrate that the proposed method is computationally stable, mass conservative and positivity preserving, in addition to the high computational efficiency on structured Yin–Yang grids.