Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations
SIAM Journal on Scientific and Statistical Computing
Generalizing the formula for areas of polygons to moments
American Mathematical Monthly
Journal of Computational Physics
Incremental remapping as a transport&slash;advection algorithm
Journal of Computational Physics
Second-order sign-preserving conservative interpolation (remapping) on general grids
Journal of Computational Physics
A forward-trajectory global semi-Lagrangian transport scheme
Journal of Computational Physics
Journal of Computational Physics
The streamline subgrid integration method: I. Quasi-monotonic second-order transport schemes
Journal of Computational Physics
Finite-volume transport on various cubed-sphere grids
Journal of Computational Physics
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
Journal of Computational Physics
A class of deformational flow test cases for linear transport problems on the sphere
Journal of Computational Physics
A multistep flux-corrected transport scheme
Journal of Computational Physics
Short Note: A simple mass conserving semi-Lagrangian scheme for transport problems
Journal of Computational Physics
An analysis of 1D finite-volume methods for geophysical problems on refined grids
Journal of Computational Physics
Journal of Computational Physics
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
Journal of Computational Physics
A conservative multi-tracer transport scheme for spectral-element spherical grids
Journal of Computational Physics
Journal of Computational Physics
Hermitian Compact Interpolation on the Cubed-Sphere Grid
Journal of Scientific Computing
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A conservative multi-tracer transport algorithm on the cubed-sphere based on the semi-Lagrangian approach (CSLAM) has been developed. The scheme relies on backward trajectories and the resulting upstream cells (polygons) are approximated with great-circle arcs. Biquadratic polynomial functions are used for approximating the density distribution in the cubed-sphere grid cells. The upstream surface integrals associated with the conservative semi-Lagrangian scheme are computed as line-integrals by employing the Gauss-Green theorem. The line-integrals are evaluated using a combination of exact integrals and high-order Gaussian quadrature. The upstream cell (trajectories) information and computation of weights of integrals can be reused for each additional tracer. The CSLAM scheme is extensively tested with various standard benchmark test cases of solid-body rotation and deformational flow in both Cartesian and spherical geometry, and the results are compared with those of other published schemes. The CSLAM scheme is accurate, robust, and moreover, the edges and vertices of the cubed-sphere (discontinuities) do not affect the overall accuracy of the scheme. The CSLAM scheme exhibits excellent convergence properties and has an option for enforcing monotonicity. The advantages of introducing cross-terms in the fully two-dimensional biquadratic density distribution functions are also examined in the context of Cartesian as well as the cubed-sphere grid which has six local sub-domains with discontinuous edges and corners.