Matthew R. Norman, North Carolina State University


Conservative Remapping with Adaptive Subgrid Approximations: Application to Conservative Semi-Lagrangian Transport

Abstract: Conservative remapping is the process of transferring a structured quantity from one mesh to another while conserving the global and local data integrals. The present study improves this process by constructing a more accurate description of the subgrid data distribution. Typically, the Piecewise Parabolic Method (PPM) with a preprocessing monotonic limiter is used to approximate the subgrid variation, and it is generally fourth-order accurate. However, PPM degenerates in accuracy when local extrema and steep jumps are present in the data. A method called the Piecewise Hyperbolic Method (PHM) was adapted to the conservative remapping context; and though it is generally only third-order accurate, it retains full accuracy at steep jumps. Therefore, a new adaptive method called PPM-Hybrid (PPM-H) was created wherein PPM is used for smooth data and extrema and PHM is used for steep jumps. Some further adaptive limiting was applied to keep the solution essentially monotonic and positive definite. To test PPM-H accuracy relative to that of PPM, the remapping procedure was implemented to perform conservative semi-Lagrangian (SL) transport of mass across a grid. Semi-Lagrangian transport consists of tracing structured grid cells upstream to their departure locations and remapping the mass from the structured grid to the departure grid. Then, the departure cell mass values simply replace the arrival cells to perform the transport of mass. For the SL application, PPM-H showed consistent and robust improvement over PPM for 1-D, 2-D Cartesian, and 2-D spherical transport problems using smooth and non-smooth data. This improvement can be carried over into other remapping applications such as conservative grid-to-grid interpolation and remapping of excessively deformed Lagrangian coordinates back to a reference grid.

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