An entropic fourier method for the Boltzmann equation
For researchers in kinetic theory and computational fluid dynamics, this method combines the advantages of discrete velocity methods (positivity, H-theorem) with the efficiency of Fourier methods (FFT), addressing a known trade-off in numerical solvers for the Boltzmann equation.
The paper introduces an entropic Fourier method for discretizing the Boltzmann collision operator that preserves positivity and satisfies a discrete H-theorem while enabling FFT-based fast algorithms, with second-order convergence validated numerically.
We propose an entropic Fourier method for the numerical discretization of the Boltzmann collision operator. The method, which is obtained by modifying a Fourier Galerkin method to match the form of the discrete velocity method, can be viewed both as a discrete velocity method and as a Fourier method. As a discrete velocity method, it preserves the positivity of the solution and satisfies a discrete version of the H-theorem. As a Fourier method, it allows one to readily apply the FFT-based fast algorithms. A second-order convergence rate is validated by numerical experiments