Adaptive Particle / Panel Methods for Global Geophysical Flow

Abstract:

We present a Lagrangian particle / panel method for geophysical fluid flow on the sphere. The spatial discretization is a set of Lagrangian fluid particles organized into panels to perform quadrature computations. Particles carry vorticity and velocity is found using the Biot-Savart integral derived from the stream function. Adaptive panel refinement and a new remeshing procedure are applied to reduce the computational cost and maintain accuracy as the flow evolves. We present solutions to the linear advection equation and the forced barotropic vorticity equation for test cases related to atmospheric and oceanic modeling including Rossby-Haurwitz waves, perturbed zonal jets, and polar vortex simulations. Development of an extension of the method to the shallow water equations is discussed.