A Pseudo-Spectral Method for Self-Gravitating Fluid Dynamics
Jane Smith, C. Mathematician
Journal of Computational Physics, 2023
We develop a pseudo-spectral method for solving the coupled Poisson–Euler system describing self-gravitating fluid dynamics in three dimensions. The algorithm achieves spectral accuracy for smooth problems and scales as O(N log N) per timestep via fast transforms, representing a significant speedup over conventional finite-volume approaches. We validate the method on a suite of test problems including Jeans instability, soliton propagation, and collapse of a cold cloud, and demonstrate sub-percent energy conservation over hundreds of dynamical times.