Polynomial interpolation schemes for internal derivative distributions on structured grids
The problem of finding interpolation schemes for a given function distribution on a two-dimensional grid, eventually involves interpolation over the corresponding derivative field. The author obtains a formulation of certain schemes which may produce smooth distributions, accurate results, and computational efficiency. Smoothness property is required because discontinuities in slope cannot be admitted when flow fields are modeled as nonlinear functions. In this direction bicubic, biquintic, cubic-linear and quintic-cubic schemes are considered to interpolate over both function and derivative fields. Some numerical results allow the reader to appraise a method as compared with another. Astrophysical \(N\)-body computations and particle trajectories in oceanic flows are discussed in details as two outstanding applications of these techniques.
scientific article; zbMATH DE number 770319