A non‐oscillatory multimoment finite‐volume global transport model on a cubed‐sphere grid using the WENO slope limiter

Abstract

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.