A characteristic mapping method for incompressible hydrodynamics on a rotating sphere

2023/02/02 by Seth T. Taylor, Taylor, Seth, Jean‐Christophe Nave +1 · 1 citation
Engineering · Earth and Planetary Sciences · #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.2302.01205

Abstract

We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as a composition of sub-interval flows formed by C¹ spherical spline interpolants. This approximation technique has the capacity of resolving sub-grid scales generated over time without increasing the spatial resolution of the computational grid. The numerical method is analyzed and validated using standard test cases yielding third-order accuracy in the supremum norm. Numerical experiments illustrating the unique resolution properties of the method are performed and demonstrate the ability to reproduce the forward energy cascade at sub-grid scales by upsampling the numerical solution.

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