High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Multidimensional flux-limited advection schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A synchronous and iterative flux-correction formalism for coupled transport equations
Journal of Computational Physics
Incremental remapping as a transport&slash;advection algorithm
Journal of Computational Physics
Journal of Computational Physics
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
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
A class of deformational flow test cases for linear transport problems on the sphere
Journal of Computational Physics
A class of deformational flow test cases for linear transport problems on the sphere
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
3DFLUX: A high-order fully three-dimensional flux integral solver for the scalar transport equation
Journal of Computational Physics
A conservative multi-tracer transport scheme for spectral-element spherical grids
Journal of Computational Physics
Hi-index | 31.48 |
A conservative semi-Lagrangian cell-integrated transport scheme (CSLAM) was recently introduced, which ensures global mass conservation and allows long timesteps, multi-tracer efficiency, and shape preservation through the use of reconstruction filtering. This method is fully two-dimensional so that it may be easily implemented on non-cartesian grids such as the cubed-sphere grid. We present a flux-form implementation, FF-CSLAM, which retains the advantages of CSLAM while also allowing the use of flux-limited monotonicity and positivity preservation and efficient tracer sub-cycling. The methods are equivalent in the absence of flux limiting or reconstruction filtering. FF-CSLAM was found to be third-order accurate when an appropriately smooth initial mass distribution and flow field (with at least a continuous second derivative) was used. This was true even when using highly deformational flows and when the distribution is advected over the singularities in the cubed sphere, the latter a consequence of the full two-dimensionality of the method. Flux-limited monotonicity preservation, which is only available in a flux-form method, was found to be both less diffusive and more efficient than the monotone reconstruction filtering available to CSLAM. Despite the additional overhead of computing fluxes compared to CSLAM's cell integrations, the non-monotone FF-CSLAM was found to be at most only 40% slower than CSLAM for Courant numbers less than one, with greater overhead for successively larger Courant numbers.