Galerkin-Petrov approach for the Boltzmann equation

TL;DR

This paper introduces a novel Galerkin-Petrov numerical method for solving the spatially homogeneous Boltzmann equation, utilizing Laguerre polynomials and spherical harmonics for improved approximation.

Contribution

It presents a new Galerkin-Petrov approach combining Laguerre polynomials and spherical harmonics, with a detailed numerical implementation for the Boltzmann equation.

Findings

Demonstrates the effectiveness of the method through numerical tests

Provides a stable and accurate algorithm for the Boltzmann equation

Shows potential for efficient computational solutions

Abstract

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.