%0 Online Multimedia %A Shaw, James %D 2017 %T Advection for steep slopes and arbitrary meshes (PDEs 2017) %U https://figshare.com/articles/presentation/Advection_for_steep_slopes_and_arbitrary_meshes/4833554 %R 10.6084/m9.figshare.4833554.v2 %2 https://ndownloader.figshare.com/files/8023577 %K advection %K cut cells %K terrain following %K Finite Volume Method %K Numerical Solution of Differential and Integral Equations %X Representing 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.