Conservative Numerical Schemes with Optimal Dispersive Wave Relations: Part II. Numerical Evaluations

  title={Conservative Numerical Schemes with Optimal Dispersive Wave Relations: Part II. Numerical Evaluations},
  author={Qingshan Chen and Lili Ju and Roger Temam},
  journal={Journal of Scientific Computing},
A new energy and enstrophy conserving scheme (EEC) for the shallow water equations is proposed and evaluated using a suite of test cases over the global spherical or bounded domain. The evaluation is organized around a set of pre-defined properties: accuracy of individual operators, accuracy of the whole scheme, conservation of key quantities, control of the divergence variable, representation of the energy and enstrophy spectra, and simulation of nonlinear dynamics. The results confirm that… 



A Potential Enstrophy and Energy Conserving Numerical Scheme for Solution of the Shallow-Water Equations on a Geodesic Grid

Abstract Using the shallow water equations, a numerical framework on a spherical geodesic grid that conserves domain-integrated mass, potential vorticity, potential enstrophy, and total energy is

A Potential Enstrophy and Energy Conserving Scheme for the Shallow Water Equations

Abstract To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed

Effects of using a posteriori methods for the conservation of integral invariants. [for weather forecasting]

Abstract An examination is made on the nature and effect of using a posteriors adjustments on nonconservative finite-difference schemes to enforce integral invariants of the corresponding analytic

A Scale-Invariant Formulation of the Anticipated Potential Vorticity Method

AbstractThe long-term success of climate models that operate on multiresolution grids depends on access to subgrid parameterizations that act appropriately across a wide range of spatial and temporal

A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal-icosahedral and cubed-sphere grids

Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a

An initial-value problem for testing numerical models of the global shallow-water equations

This new test case is intended to serve as a complement to the Williamson et al. suite, and should be of particular interest in that it involves the formation of complicated dynamical features similar to those that arise in numerical weather prediction and climate models.

A shallow water model conserving energy and potential enstrophy in the presence of boundaries

We extend a previously developed method for constructing shallow water models that conserve energy and potential enstrophy to the case of flow bounded by rigid walls. This allows the method to be