This project explores a mesh-free method for the approximations of Numerical Operators for 2D and 3D partial differential equations used in atmospheric dynamics. Compactly Supported Radial Basis Functions were chosen as the category of Mesh Free method for discretization. The primary objective of this project is to formulate a highly parallel algorithm. The secondary objective is to test the capabilities of a framework of powerful libraries such as Atlas/Atlas4Py which is developed by ECMWF; BLAS and SuperLU. The uniqueness in the project stems from having a singular focus on achieving a computationally intensive problem statement. The ultimate objective is to create a challenge that demands the immense computational power of high-performance computer architecture, enabling rapid and efficient execution of complex computations. The performance of the python implementation is tested using standard test cases provided by David J. Williamson and et al. for Numerical Approximations of Shallow Water Equation (SWE) on a spherical geometry. In conclusion, this project aims to provide a package of powerful tools capable to solve 2D and 3D PDEs related to atmospheric dynamics such as the shallow water equations, the hydrostatic primitive equations, and the non-hydrostatic fully-compressible Euler equations using mesh-free operators.