Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Direct discretization of planar div-curl problems
SIAM Journal on Numerical Analysis
Multidimensional flux-limited advection schemes
Journal of Computational Physics
Conservation properties of unstructured staggered mesh schemes
Journal of Computational Physics
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Some conservation issues for the dynamical cores of NWP and climate models
Journal of Computational Physics
Numerical representation of geostrophic modes on arbitrarily structured C-grids
Journal of Computational Physics
Journal of Computational Physics
Inspection of hexagonal and triangular C-grid discretizations of the shallow water equations
Journal of Computational Physics
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
A co-volume scheme for the rotating shallow water equations on conforming non-orthogonal grids
Journal of Computational Physics
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 | 31.49 |
A numerical scheme applicable to arbitrarily-structured C-grids is presented for the nonlinear shallow-water equations. By discretizing the vector-invariant form of the momentum equation, the relationship between the nonlinear Coriolis force and the potential vorticity flux can be used to guarantee that mass, velocity and potential vorticity evolve in a consistent and compatible manner. Underpinning the consistency and compatibility of the discrete system is the construction of an auxiliary thickness equation that is staggered from the primary thickness equation and collocated with the vorticity field. The numerical scheme also exhibits conservation of total energy to within time-truncation error. Simulations of the standard shallow-water test cases confirm the analysis and show convergence rates between 1st- and 2nd-order accuracy when discretizing the system with quasi-uniform spherical Voronoi diagrams. The numerical method is applicable to a wide class of meshes, including latitude-longitude grids, Voronoi diagrams, Delaunay triangulations and conformally-mapped cubed-sphere meshes.