Xu, D. S., D. H. Chen, and K. X. Wu, 2021: Properties of high-order finite difference schemes and idealized numerical testing. Adv. Atmos. Sci., 38(4), 615−626, https://doi.org/10.1007/s00376-020-0130-7.
Citation: Xu, D. S., D. H. Chen, and K. X. Wu, 2021: Properties of high-order finite difference schemes and idealized numerical testing. Adv. Atmos. Sci., 38(4), 615−626, https://doi.org/10.1007/s00376-020-0130-7.

Properties of High-Order Finite Difference Schemes and Idealized Numerical Testing

  • Construction of high-order difference schemes based on Taylor series expansion has long been a hot topic in computational mathematics, while its application in comprehensive weather models is still very rare. Here, the properties of high-order finite difference schemes are studied based on idealized numerical testing, for the purpose of their application in the Global/Regional Assimilation and Prediction System (GRAPES) model. It is found that the pros and cons due to grid staggering choices diminish with higher-order schemes based on linearized analysis of the one-dimensional gravity wave equation. The improvement of higher-order difference schemes is still obvious for the mesh with smooth varied grid distance. The results of discontinuous square wave testing also exhibits the superiority of high-order schemes. For a model grid with severe non-uniformity and non-orthogonality, the advantage of high-order difference schemes is inapparent, as shown by the results of two-dimensional idealized advection tests under a terrain-following coordinate. In addition, the increase in computational expense caused by high-order schemes can be avoided by the precondition technique used in the GRAPES model. In general, a high-order finite difference scheme is a preferable choice for the tropical regional GRAPES model with a quasi-uniform and quasi-orthogonal grid mesh.
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