An Upwind-Biased Conservative Transport Scheme for Multistage Temporal Integrations on Spherical Icosahedral Grids

AbstractA standard nominally third-order upwind-biased spatial discretization of the flux-divergence operator was extended to a spherical icosahedral grid. The method can be used with multistage time-stepping schemes such as the Runge–Kutta method to compute the transport of variables on both hexagonal–pentagonal and triangular meshes. Two algorithms can be used to determine mesh cell face values: 1) interpolation using a quadratic function reconstructed subject to an integral constraint, or 2) calculation of the weighted mean of two linearly interpolated and extrapolated values. The first approach was adopted for a triangular mesh because the second approach depends on the mesh having a hexagonal or pentagonal shape. Both approaches were tested on the hexagonal–pentagonal mesh.These schemes were subjected to standard transport tests on a spherical icosahedral grid. A three-stage Runge–Kutta time stepping method was used, and if necessary a flux limiter was applied to maintain monotonicity. The two differ...

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