Source terms for shallow water on the sphereΒΆ

The shallow water equations on the sphere involve some geometric source terms that are currently missing from GeoClaw. Experiments during initial develpment of GeoClaw seemed to indicate that they were not important, but more recently it has been found that at least the source term in the mass equation can be quite important for properly modeling waves moving between the tropics and polar regions due to the variation in cell size with latitude.

As of v5.9.1, these source terms have been added to $CLAW/geoclaw/src/2d/shallow/src2.f90. There is a parameter rundata.geo_data.sphere_source that can be set to 0 for no source terms, 1 to add the source term only in the mass equation, or 2 to add source terms in the momentum equations too.

Change in default behavior:

Starting in v5.10.0, the default value

rundata.geo_data.sphere_source = 1

is used if this parameter is not set otherwise in, so that the source term in mass is included. Adding the source terms in momentum seems to have almost no effect in most practical problems, as illustrated in this document, which presents more discussion of these source terms and includes some examples to illustrate the effect they have in various circumstances.