Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
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
A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM)
Journal of Computational Physics
Journal of Computational Physics
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A quartic spline based remapping algorithm is developed and illustrative tests of it are presented herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed quartic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A high-order grid and sub-grid based monotonic filter is also incorporated into the overall scheme. This filter is independent of the underlying spline representation adopted here, and is of more general application.