The Discretization-Corrected Particle Strength Method for the Barotropic Vorticity Equations

We present a novel meshless Lagrangian method for numerically solving the barotropic vorticity equation on a rotating sphere, an essential model in geophysical fluid dynamics. Our approach combines a particle-based discretization with a Discretization Corrected Particle Strength Exchange (DCPSE) operator, offering a consistent and accurate approximation of differential operators on unstructured node distributions. The method is implemented in a fully Lagrangian framework, inherently conserving circulation and enabling straightforward adaptation to complex geometries. We validate the proposed scheme against standard test cases for global circulation and Rossby-Haurwitz waves. The results demonstrate excellent agreement with reference solutions obtained from high-resolution spectral and finite difference models. In particular, our method captures the essential dynamics of the vorticity field with high fidelity and low numerical diffusion, while exhibiting convergence and stability properties suitable for long-term integrations. This study highlights the potential of meshless Lagrangian techniques in large-scale geophysical simulations. These techniques provide an alternative to traditional grid-based approaches and facilitate the natural handling of adaptive and irregular node distributions.