2022/04/26 by Tino Franz, Franz, Tino
Engineering · Mathematics · #65M12 #65M70 #76D05 #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2204.12379
openalex publication_date 2022/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we develop a high-order collocation method using radial basis function (RBF) for the incompressible Navier-Stokes equation (NSE) on the rotating sphere. The method is based on solving the projection of the NSE on the space of divergence-free functions. For that, we use matrix valued kernel functions which allow an analytically divergence-free approximation of the velocity field. Using kernel functions which lead to rotation-free approximations, the pressure can be recovered by a simple kernel exchange in one of the occurring approximations, without solving an additional Poisson problem. We establish precise error estimates for the velocity and the pressure functions for the semi-discretised solution. In the end, we give a short estimate of the numerical cost and apply the new method to an experimental test case.