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Second-order sign-preserving conservative interpolation (remapping) on general grids. (English) Zbl 1016.65004
Summary: An accurate conservative interpolation (remapping) algorithm is an essential component of most arbitrary Lagrangian-Eulerian methods. We describe a local remapping algorithm for a positive scalar function. This algorithm is second-order accurate, conservative, and sign preserving. The algorithm is based on estimating the mass exchanged between cells at their common interface, and so is equally applicable to structured and unstructured grids. We construct the algorithm in a series of steps, clearly delineating the assumptions and errors made at each step. We validate our theory with a suite of numerical examples, analyzing the results from the viewpoint of accuracy and order of convergence.

MSC:
65D05 Numerical interpolation
Software:
REMAP3D; MPDATA
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