skip to content

Slope-limited transport schemes using icosahedral hexagonal grid

Tuesday 25th September 2012 - 09:00 to 09:25
INI Seminar Room 1
Session Title: 
Advection Session
In this work two simple advection schemes for unstructured meshes are proposed and implemented over spherical icosahedral-hexagonal grids. One of them is fully discrete in space and time while the other one is a semi discrete scheme with third order RungeKutta time integration. Both schemes use cell-wise linear reconstruction. We therefore also present 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 a special grid optimization. Monotonicity of the advection schemes is enforced by a slope limiter, at contrast with the widely used of posterior approach of flux-corrected transport (FCT). Convergence of the proposed gradient reconstruction operators is verified numerically. It is found that the proposed modification is indeed necessary for convergence on non-optimized grids. Recently proposed advection test cases are used to evaluate the performance of the slope-limited advection schemes. It is verified that they are convergent and positive. We also compare these schemes to a variant where positivity is enforced by the FCT approach. FCT produces slightly less diffusion but it seems to be at the price of some nonphysical anti-diffusion. These results suggest that the proposed slope limited advection schemes are a viable option for icosahedral-hexagonal grids over sphere.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons