Inherently Conservative Nonpolynomial-Based Remapping Schemes: Application to Semi-Lagrangian Transport

Abstract A group of new conservative remapping schemes based on nonpolynomial approximations is proposed. The remapping schemes rely on the conservative cascade scheme (CCS), which employs an efficient sequence of 1D remapping operations to solve a multidimensional problem. The present study adapts three new nonpolynomial-based reconstructions of subgrid variation to the CCS: the Piecewise Hyperbolic Method (PHM), the Piecewise Double Hyperbolic Method (PDHM), and the Piecewise Rational Method (PRM) for comparison with the baseline method: the Piecewise Parabolic Method (PPM). Additionally, an adaptive hybrid approximation scheme, PPM-Hybrid (PPM-H), is constructed using monotonic PPM for smooth data and local extrema and using PHM for steep jumps where PPM typically suffers large accuracy degradation because of its original monotonic filter. Smooth and nonsmooth data profiles are transported in 1D, 2D Cartesian, and 2D spherical frameworks under uniform advection, solid-body rotation, and deformational f...

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