Direct discretization of planar div-curl problems
SIAM Journal on Numerical Analysis
Support-operator finite-difference algorithms for general elliptic problems
Journal of Computational Physics
Spectral transform solutions to the shallow water test set
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Applied Numerical Mathematics
The continuous Galerkin method is locally conservative
Journal of Computational Physics
Parallel Semi-Implicit Spectral Element Methods for Atmospheric General Circulation Models
Journal of Scientific Computing
Multiscale Geophysical Modeling Using the Spectral Element Method
Computing in Science and Engineering
International Journal of High Performance Computing Applications
The NCAR Spectral Element Climate Dynamical Core: Semi-Implicit Eulerian Formulation
Journal of Scientific Computing
Journal of Computational Physics
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
Journal of Computational Physics
High-performance high-resolution semi-Lagrangian tracer transport on a sphere
Journal of Computational Physics
CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model
International Journal of High Performance Computing Applications
Journal of Computational Physics
MCore: A non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods
Journal of Computational Physics
Dispersive behaviour of high order finite element schemes for the one-way wave equation
Journal of Computational Physics
Hi-index | 31.47 |
We derive a formulation of the spectral element method which is compatible on very general unstructured three-dimensional grids. Here compatible means that the method retains discrete analogs of several key properties of the divergence, gradient and curl operators: the divergence and gradient are anti-adjoints (the negative transpose) of each other, the curl is self-adjoint and annihilates the gradient operator, and the divergence annihilates the curl. The adjoint relations hold globally, and at the element level with the inclusion of a natural discrete element boundary flux term. We then discretize the shallow-water equations on the sphere using the cubed-sphere grid and show that compatibility allows us to locally conserve mass, energy and potential vorticity. Conservation is obtained without requiring the equations to be in conservation form. The conservation is exact assuming exact time integration.