pdes2017-jshaw.pptx (13.61 MB)
Advection for steep slopes and arbitrary meshes (PDEs 2017)
Version 2 2017-04-09, 15:34
Version 1 2017-04-09, 15:29
presentation
posted on 2017-04-09, 15:34 authored by James ShawJames ShawRepresenting terrain in atmospheric models creates mesh distortions that
increase advection errors and pressure gradient errors. Finer meshes are able
to resolve steep slopes that result in larger distortions and increased numerical
errors. Smoothing terrain-following coordinates can help to reduce distortions,
and the cut cell method reduces distortions even further, but creates arbitrarily
small cut cells that can severely constrain the time-step for explicit methods.
Regardless of the mesh type, distortions can only be reduced, not eliminated.
We present two new methods that improve the accuracy of flows over steep
terrain on arbitrarily-structured meshes. First, the slanted cell mesh is a new
method that avoids additional time-step constraints derived from a von Neumann
analysis to ensure numerical stability on severely distorted meshes.
The method-of-lines advection scheme is assessed using a new test case in
which a tracer placed at the ground is transported over steep mountains. We
find that the scheme is largely insensitive to the type of mesh and steepness of
the mountains. We also demonstrate that the scheme is second-order convergent
irrespective of mesh distortions. Incorporating the new advection scheme into a
dynamical core we show that, compared to terrain-following and cut cell meshes,
the slanted cell mesh reduces pressure gradient errors.