A Generalized Z-Grid Numerical Prediction Model for Improving Stability and Efficiency

Among staggered gridded finite volume numerical prediction models, a Z-grid scheme has better dispersion relation and less computational modes. It uses vorticity and divergence for momentum equations and relatively more natural to implement on a sphere. We propose a generalization of a Voronoi based Z-grid scheme for further improving its stability and efficiency while maintaining its other important numerical advantages. Instead of using Voronoi centers, the generalized scheme uses centroid centers and wider stencils. Even though we plan to implement this scheme for a sphere, we performed some numerical experiments of shallow water equations on a plane first comparing the generalized scheme to the standard Voronoi Z-grid. We found the new scheme is more stable and can take longer time steps in temporal integration. In this presentation, we will introduce the generalization scheme, show its dispersion relation analysis, and report our numerical results of some standard and more rigorous test cases in order to demonstrate the stability and efficiency.