Fast spectral Boltzmann solvers: where they shine, where they stop, and what industry actually needs
Published:
The Boltzmann collision operator is one of the most expensive pieces of kinetic theory. In three velocity dimensions, a naive quadrature costs on the order of (N^6) operations per evaluation, where (N) is the resolution in each direction. For decades, that cost made full deterministic kinetic simulations impractical outside academic benchmarks. Fast spectral methods changed the picture—not by simplifying the physics, but by exploiting the convolution structure hidden inside the collision integral.