Surface grid generation based on elliptic PDE models
Applied Mathematics and Computation - Special issue on differential equations and computational simulations I
Journal of Computational Physics
Computational conformal mapping for surface grid generation
Journal of Computational Physics
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
Global Weather Prediction and High-End Computing at NASA
Computing in Science and Engineering
International Journal of High Performance Computing Applications
Journal of Computational Physics
A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid
Journal of Computational Physics
Journal of Computational Physics
High-order finite-volume methods for the shallow-water equations on the sphere
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes
SIAM Journal on Scientific Computing
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
On simplifying 'incremental remap'-based transport schemes
Journal of Computational Physics
High-performance high-resolution semi-Lagrangian tracer transport on a sphere
Journal of Computational Physics
A general method for modeling on irregular grids
International Journal of High Performance Computing Applications
Geometric Properties of the Icosahedral-Hexagonal Grid on the Two-Sphere
SIAM Journal on Scientific Computing
Improving the performance scalability of the community atmosphere model
International Journal of High Performance Computing Applications
MCore: A non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods
Journal of Computational Physics
High Order Finite Difference and Finite Volume Methods for Advection on the Sphere
Journal of Scientific Computing
Mixed finite elements for numerical weather prediction
Journal of Computational Physics
Argonne applications for the IBM Blue Gene/Q, Mira
IBM Journal of Research and Development
A finite element exterior calculus framework for the rotating shallow-water equations
Journal of Computational Physics
Hermitian Compact Interpolation on the Cubed-Sphere Grid
Journal of Scientific Computing
Hi-index | 31.50 |
The performance of a multidimensional finite-volume transport scheme is evaluated on the cubed-sphere geometry. Advection tests with prescribed winds are used to evaluate a variety of cubed-sphere projections and grid modifications including the gnomonic and conformal mappings, as well as two numerically generated grids by an elliptic solver and spring dynamics. We explore the impact of grid non-orthogonality on advection tests over the corner singularities of the cubed-sphere grids, using some variations of the transport scheme, including the piecewise parabolic method with alternative monotonicity constraints. The advection tests revealed comparable or better accuracy to those of the original latitudinal-longitudinal grid implementation. It is found that slight deviations from orthogonality on the modified cubed-sphere (quasi-orthogonal) grids do not negatively impact the accuracy. In fact, the more uniform version of the quasi-orthogonal cubed-sphere grids provided better overall accuracy than the most orthogonal (and therefore, much less uniform) conformal grid. It is also shown that a simple non-orthogonal extension to the transport equation enables the use of the highly non-orthogonal and computationally more efficient gnomonic grid with acceptable accuracy.