Poisson quadrature method of moments for 2D kinetic equations with velocity of constant magnitude

TL;DR

This paper introduces Poisson-EQMOM, a novel quadrature method of moments for 2D kinetic equations with constant velocity magnitude, featuring convergence guarantees and validated through numerical tests on the Vicsek model.

Contribution

The paper develops a new Poisson kernel-based moment closure method with proven convergence for 2D kinetic equations with fixed velocity magnitude.

Findings

Method converges as the number of moments increases.

Validated with numerical tests on the Vicsek model.

Applicable to spatially homogeneous and multi-dimensional problems.

Abstract

This work is concerned with kinetic equations with velocity of constant magnitude. We propose a quadrature method of moments based on the Poisson kernel, called Poisson-EQMOM. The derived moment closure systems are well defined for all physically relevant moments and the resultant approximations of the distribution function converge as the number of moments goes to infinity. The convergence makes our method stand out from most existing moment methods. Moreover, we devise a delicate moment inversion algorithm. As an application, the Vicsek model is studied for overdamped active particles. Then the Poisson-EQMOM is validated with a series of numerical tests including spatially homogeneous, one-dimensional and two-dimensional problems.