By using CSL3 multimoment interpolation, a piecewise cubic polynomial for spatial reconstruction can be obtained with four multimoment constraint conditions consisting of two point values at cell boundaries, one volume-integrated average and one slope parameter at the cell center. The resulting multimoment finite-volume scheme is of fourth-order accuracy. A non-oscillatory scheme can be derived by designing the proper formula to calculate the slope parameter at the cell center. A new strategy was recently proposed, using the Weighted Essentially Non-Oscillatory (WENO) concept to determine the slope parameter. Using a WENO-type limiter, the multimoment reconstruction can effectively remove nonphysical oscillations while keeping fourth-order accuracy in smooth regions. In this study, a WENO-type slope limiter is proposed and implemented in our multimoment finite-volume global transport model based on the cubed-sphere grid. The widely used benchmark tests, including both solid rotation and complicated deformational advection cases, are checked to verify the performance of the proposed global transport model. Numerical results reveal that a WENO-type slope limiter can greatly improve the accuracy of the multimoment finite-volume model compared with the former Total Variation Diminishing (TVD)-type limiter. Furthermore, the proposed limiter is constructed over a compact stencil of only three adjacent cells. Without any user-defined or problem-dependent parameters, the present model is very promising for practical applications. KEYWORDS cubed-sphere grid; global model; multimoment scheme; slope limiter; transport model; WENO
INTRODUCTIONDue to polar problems on the latitude-longitude grid, global computational meshes with a quasi-uniform grid spacing and free of polar problems, such as the cubed-sphere grid (Sadourny, 1972), icosahedral grid (Sadourny et al., 1968;Williamson, 1968), and yin-yang grid (Kageyama and Sato, 2004), are becoming popular in constructing global models, especially for those aiming at very high-resolution simulations of atmospheric dynamics. One of the key issues in implementing research and operational models on these quasi-uniform grids is the relatively complex grid structure, which causes essential difficulties in constructing high-order models and introduces extra grid-imprinting errors. In the past decade, some accurate global models have been proposed on these grids through the application of so-called "local" schemes, such as the discontinuous Galerkin scheme (Nair et al., 2005a;2005b), the spectral element scheme (Dennis et al., 2012), the multimoment scheme (Chen et al., 2014) and so on. These schemes are accomplished based on compact stencils (usually within a single computational element) and are very convenient to implement in spherical geometry to develop high-order models. Furthermore, these schemes are computationally intensive, so they are highly scalable on massively parallel clusters. A comprehensive review on the applications of quasi-uniform grids can be found in the work of...