Numerical Testing of a New Positivity-Preserving Interpolation Algorithm

TL;DR

This paper introduces a new positivity-preserving interpolation algorithm tested numerically, demonstrating its effectiveness in maintaining positivity and accuracy when interpolating between different spatial grids, especially in weather prediction models.

Contribution

The paper presents a novel positivity-preserving interpolation algorithm designed for use with spectral element and cartesian meshes, addressing a key challenge in numerical weather prediction models.

Findings

The new algorithm maintains positivity across various test problems.

It achieves accuracy comparable to existing methods.

It is effective in complex grid coupling scenarios.

Abstract

An important component of a number of computational modeling algorithms is an interpolation method that preserves the positivity of the function being interpolated. This report describes the numerical testing of a new positivity-preserving algorithm that is designed to be used when interpolating from a solution defined on one grid to different spatial grid. The motivating application for this work was a numerical weather prediction (NWP) code that uses a spectral element mesh discretization for its dynamics core and a cartesian tensor product mesh for the evaluation of its physics routines. This coupling of spectral element mesh, which uses nonuniformly spaced quadrature/collocation points, and uniformly-spaced cartesian mesh combined with the desire to maintain positivity when moving between these meshes necessitates our work. This new approach is evaluated against several typical algorithms in use on a range of test problems in one or more space dimensions. The results obtained show that the new method is competitive in terms of observed accuracy while at the same time preserving the underlying positivity of the functions being interpolated.