New icosahedral grid-point discretizations of the shallow water equations on the sphere
Journal of Computational Physics
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations
Journal of Computational Physics
Numerical wave propagation on the hexagonal C-grid
Journal of Computational Physics
Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
An analysis of 1D finite-volume methods for geophysical problems on refined grids
Journal of Computational Physics
Inspection of hexagonal and triangular C-grid discretizations of the shallow water equations
Journal of Computational Physics
Numerical wave propagation for the triangular P1DG-P2 finite element pair
Journal of Computational Physics
Mixed finite elements for numerical weather prediction
Journal of Computational Physics
Spurious inertial oscillations in shallow-water models
Journal of Computational Physics
Journal of Computational Physics
A co-volume scheme for the rotating shallow water equations on conforming non-orthogonal grids
Journal of Computational Physics
A finite element exterior calculus framework for the rotating shallow-water equations
Journal of Computational Physics
Improved smoothness and homogeneity of icosahedral grids using the spring dynamics method
Journal of Computational Physics
Hi-index | 31.50 |
A C-grid staggering, in which the mass variable is stored at cell centers and the normal velocity component is stored at cell faces (or edges in two dimensions) is attractive for atmospheric modeling since it enables a relatively accurate representation of fast wave modes. However, the discretization of the Coriolis terms is non-trivial. For constant Coriolis parameter, the linearized shallow water equations support geostrophic modes: stationary solutions in geostrophic balance. A naive discretization of the Coriolis terms can cause geostrophic modes to become non-stationary, causing unphysical behaviour of numerical solutions. Recent work has shown how to discretize the Coriolis terms on a planar regular hexagonal grid to ensure that geostrophic modes are stationary while the Coriolis terms remain energy conserving. In this paper this result is extended to arbitrarily structured C-grids. An explicit formula is given for constructing an appropriate discretization of the Coriolis terms. The general formula is illustrated by showing that it recovers previously known results for the planar regular hexagonal C-grid and the spherical longitude-latitude C-grid. Numerical calculation confirms that the scheme does indeed give stationary geostrophic modes for the hexagonal-pentagonal and triangular geodesic C-grids on the sphere.