Adaptive particle methods for barotropic vorticity dynamics on a rotating sphere

We present an adaptive particle method for barotropic vorticity dynamics on a rotating sphere. The flow map is represented by Lagrangian particles, organized into either triangular icosahedral panels or cubed-sphere quadrilateral panels. The particles carry vorticity and the panels are used to obtain quadrature weights in the point vortex approximation of the Biot-Savart integral. Adaptive panel refinement and remeshing are applied to maintain accuracy and reduce computational cost. Examples include Rossby-Haurwitz waves, Gaussian vortices, and perturbed jet dynamics.