DeepAI AI Chat
Log In Sign Up

On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation

11/11/2020
by   Lorenzo Pareschi, et al.
0

Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong long time behavior. A way to overcome this drawback, without sacrificing spectral accuracy, has been proposed recently with the construction of equilibrium preserving spectral methods. Despite the ability to capture the steady state with arbitrary accuracy, the theoretical properties of the method have never been studied in details. In this paper, using the perturbation argument developed by Filbet and Mouhot for the homogeneous Boltzmann equation, we prove stability, convergence and spectrally accurate long time behavior of the equilibrium preserving approach.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/27/2021

Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation

Spectral methods, thanks to the high accuracy and the possibility of usi...
05/18/2021

A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions

Numerical approximation of the Boltzmann equation presents a challenging...
09/26/2018

A Discontinuous Galerkin Fast Spectral Method for the Full Boltzmann Equation with General Collision Kernels

The Boltzmann equation, an integro-differential equation for the molecul...
04/23/2020

A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels

We introduce a fast Fourier spectral method for the spatially homogeneou...
09/04/2016

Spectral learning of dynamic systems from nonequilibrium data

Observable operator models (OOMs) and related models are one of the most...