This thesis explores iterative methods for solving elliptic partial differential equations (PDEs), which are used in computational fluid dynamics (CFD) to model a wide range of physical phenomena. The primary application of interest here is self-gravity, modeled by Poisson’s equation. Although many numerical approaches exist, including direct matrix inversion, FFT-based methods, and classical iterative methods such as Jacobi and Gauss-Seidel, these approaches involve tradeoffs in computational cost, scalability, implementation complexity, and adaptability to changing boundary conditions and problem configurations. Therefore, we introduce SORh, a simple and efficient relaxation method derived from a hyperbolic reformulation of Poisson’s equation. SORh generalizes classical successive […]