Eulerian and semi-Lagrangian schemes are often used to simulate the Earth’s oceans and atmosphere, but it has been proposed that a fully Lagrangian approach may be more computationally efficient in terms of simulation runtime. In this presentation, a Lagrangian particle-based framework is proposed to perform global high-resolution fluid simulations on the sphere. Our approach builds off of existing techniques that represent particles as power cells (a generalization of Voronoi cells) to simulate incompressible fluids. The efficiency of the power diagram calculation is of utmost importance since this Lagrangian framework requires calculating several power diagrams at each time step of the fluid simulation. For now, we focus on geometrical aspects of this problem, particularly the fast calculation of power diagrams on the sphere. We present a parallel technique for calculating Voronoi and power cells on the sphere by applying the radius of security theorem along with a hierarchical triangular mesh to compute the nearest neighbors of every site. Next, we compare our approach with existing techniques for computing spherical Voronoi diagrams. Depending on the distribution of the sites, our approach enables 10 million Voronoi cells to be calculated in about 12 - 15 seconds on a 10-core laptop (about 9 - 10 seconds to compute the nearest neighbors and 3 - 5 seconds to compute the Voronoi diagram), which is faster than MPI-SCVT (3x), STRIPACK (76x) and the method used by scipy.spatial.SphericalVoronoi (5x). Finally, we use our technique for calculating power diagrams to demonstrate a particle-based approach for simulating incompressible fluids on a rotating sphere using the Gallouët-Mérigot scheme and discuss future plans to extend the framework to simulate more general fluid flows.