High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Incremental remapping as a transport&slash;advection algorithm
Journal of Computational Physics
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
A forward-trajectory global semi-Lagrangian transport scheme
Journal of Computational Physics
High-order Galerkin methods for scalable global atmospheric models
Computers & Geosciences
A spectral finite volume transport scheme on the cubed-sphere
Applied Numerical Mathematics
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
Selective monotonicity preservation in scalar advection
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
Journal of Computational Physics
Mathematical and Computer Modelling: An International Journal
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
Analysis of grid imprinting on geodesic spherical icosahedral grids
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
Hi-index | 31.48 |
A class of new benchmark deformational flow test cases for the two-dimensional horizontal linear transport problems on the sphere is proposed. The scalar field follows complex trajectories and undergoes severe deformation during the simulation; however, the flow reverses its course at half-time and the scalar field returns to its initial position and shape. This process makes the exact solution available at the end of the simulation, and facilitates assessment of the accuracy of the underlying transport scheme. A procedure to eliminate possible cancellations of errors when the flow reverses is proposed. The test suite consists of four cases. Three are based on non-divergent flow fields and one on a divergent flow. The initial conditions are prescribed in terms of regular latitude-longitude spherical coordinates and are easy to implement. The divergent flow is specifically aimed for conservative global transport schemes to test for conservation, consistency and monotonicity (or positivity) of limiters/filters in a challenging flow environment. In the context of semi-Lagrangian schemes, the time-varying flow fields can be used to test trajectory algorithms where the exact trajectories do not follow great-circle arcs. The characteristics of the test cases are demonstrated with two different transport schemes.