Completely conservative and oscillationless semi-Lagrangian schemes for advection transportation
Journal of Computational Physics
A forward-trajectory global semi-Lagrangian transport scheme
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Selective monotonicity preservation in scalar advection
Journal of Computational Physics
The monotonic Quartic Spline Method (QSM) for conservative transport problems
Journal of Computational Physics
A conservative semi-Lagrangian multi-tracer transport scheme (CSLAM) on the cubed-sphere grid
Journal of Computational Physics
Short Note: A simple mass conserving semi-Lagrangian scheme for transport problems
Journal of Computational Physics
Journal of Computational Physics
An unconditionally stable fully conservative semi-Lagrangian method
Journal of Computational Physics
Hi-index | 31.48 |
The recently devised one-dimensional parabolic spline method (PSM) for efficient, conservative, and monotonic remapping is introduced into the semi-Lagrangian inherently-conserving and efficient (SLICE) scheme for transport problems in multi-dimensions. To ensure mass conservation, an integral form of the transport equation is used rather than the differential form of classical semi-Lagrangian schemes. Integrals within the SLICE scheme are computed using multiple sweeps of PSM along flow-dependent cascade directions to avoid the large timestep-dependent splitting errors associated with traditional fixed-direction splitting. Accuracy of the overall scheme, including at large timestep, is demonstrated using two-dimensional test problems in both Cartesian and spherical geometries and compared with that of the piecewise parabolic method (PPM) applied within the same SLICE framework.