Linear Properties of Numerical Schemes for the Shallow Water Equations

Christopher Eldred, Colorado State University

The shallow water equations provide a useful analog of fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. There has been extensive work exploring the linear properties (balanced states and propagating modes) of various schemes for the shallow water equations on uniform grids, but comparatively little work for nonuniform grids (especially in the case of finite difference and finite volume methods). The advantage of uniform grids is that an analytic solution often is possible. The disadvantage is that such grids are not necessarily representative of the actual grids used in dynamical cores on the sphere. Using the Shallow Water Testbed Framework (SWTF) built on top of Morphe, the linear properties of various popular finite-difference and finite-volume schemes are examined on both uniform and nonuniform grids (geodesic, cubed sphere).

Abstract Author(s): Christopher F. Eldred and David A. Randall