A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres

TL;DR

This paper introduces a pseudospectral quadrature method for solving the Navier-Stokes equations on rotating spheres, combining spectral accuracy with efficient computation techniques like FFT and adaptive time discretization.

Contribution

It develops a novel pseudospectral quadrature scheme specifically tailored for the surface Navier-Stokes equations on rotating spheres, with rigorous error analysis based on Gevrey regularity.

Findings

Spectrally accurate numerical error estimates

Efficient implementation using FFT

Stable adaptive time discretization

Abstract

In this work, we describe, analyze, and implement a pseudospectral quadrature method for a global computer modeling of the incompressible surface Navier-Stokes equations on the rotating unit sphere. Our spectrally accurate numerical error analysis is based on the Gevrey regularity of the solutions of the Navier-Stokes equations on the sphere. The scheme is designed for convenient application of fast evaluation techniques such as the fast Fourier transform (FFT), and the implementation is based on a stable adaptive time discretization.