High-Order Finite-Volume Transport on the Cubed Sphere: Comparison between 1D and 2D Reconstruction Schemes

AbstractThis paper presents two finite-volume (FV) schemes for solving linear transport problems on the cubed-sphere grid system. The schemes are based on the central-upwind finite-volume (CUFV) method, which is a class of Godunov-type method for solving hyperbolic conservation laws, and combines the attractive features of the classical upwind and central FV methods. One of the CUFV schemes is based on a dimension-by-dimension approach and employs a fifth-order one-dimensional (1D) Weighted Essentially Nonoscillatory (WENO5) reconstruction method. The other scheme employs a fully two-dimensional (2D) fourth-order accurate reconstruction method. The cubed-sphere grid system imposes several computational challenges due to its patched-domain topology and nonorthogonal curvilinear grid structure. A high-order 1D interpolation procedure combining cubic and quadratic interpolations is developed for the FV schemes to handle the discontinuous edges of the cubed-sphere grid. The WENO5 scheme is compared against th...

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