On the inter-comparison of two tracer transport schemes on icosahedral grids

摘要

Two simple finite volume advection schemes based on linear sub-grid reconstruction are implemented over spherical icosahedral-hexagonal grids. One of theses schemes is fully discrete in space and time, while the other one is a semi-discrete scheme with third order Runge-Kutta time integration. For the linear sub-grid reconstruction, we propose two possible candidates for consistent gradient discretization over general grids. These gradients are designed in a finite volume sense with an adequate modification to guarantee convergence in the absence of special grid optimization. To generate our computational mesh from triangular grid, we either use centroids (BT grid) or circumcenters (VT grid) of the spherical triangular mesh. A numerical convergence study is used to show that for a first order convergence of our discrete gradients grid modification is sufficient, whereas to achieve second order convergence grid optimization is mandatory. This study also implicates that BT grid offers a better rate of convergence than VT grid. Monotonicity of the advection schemes is enforced by a slope limiter as well as flux-corrected transport (FCT). We compared aforementioned space-time coupled and space-time decoupled advection schemes in terms of their performance for the recently proposed advection test cases. Our findings advocate that space-time coupled advection scheme is performing better than its counterpart. Furthermore, we used the fully discrete advection scheme to carried out a comparison of slope limitation and FCT approach to achieve monotonicity.