A13M-07:
Energy and Potential Enstrophy Conserving Scheme for the Rotating Shallow Water Equations on an Arbitrary Grid
Monday, 15 December 2014: 3:10 PM
Christopher Eldred, Colorado State University, Fort Collins, CO, United States and David A Randall, Colorado State University, Atmospheric Science, Fort Collins, CO, United States
Abstract:
The shallow water equations provide a useful analogue of fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. With regards to conservation properties, there have been two major thrusts of research: Hamiltonian methods (work done by Salmon and Dubos, primarily) and Discrete Exterior Calculus (DEC; Thuburn, Cotter, Ringler, etc.). In particular, recent work done by Thuburn and Cotter (2011) introduced a generalized framework for energy-conservative C-grid discretizations of the rotating shallow water equation using ideas from Discrete Exterior Calculus. The current research elucidates the connections between the Hamiltonian and DEC approaches, and looks at potential enstrophy conservation in addition to total energy conservation. As an illustration of this approach, an extension of the Arakawa and Lamb 1981 total energy and potential enstrophy conserving scheme to arbitrary, non-orthogonal polygonal grids is made.
