Galerkin-Petrov approach for the Boltzmann equation
This work provides a novel numerical method for solving the Boltzmann equation, which is important for computational physics and kinetic theory.
The authors propose a new Galerkin-Petrov method for solving the spatially homogeneous Boltzmann equation using Laguerre polynomials and spherical harmonics, demonstrating its effectiveness through numerical tests.
In this work, we propose a new Galerkin-Petrov method for the numerical solution of the classical spatially homogeneous Boltzmann equation. This method is based on an approximation of the distribution function by associated Laguerre polynomials and spherical harmonics and test an a variational manner with globally defined three-dimensional polynomials. A numerical realization of the algorithm is presented. The algorithmic developments are illustrated with the help of several numerical tests.