On quantifying uncertainties for the linearized BGK kinetic equation

TL;DR

This paper investigates how inaccuracies in the equilibrium function's velocity and temperature affect the solution of the linearized BGK kinetic equation, providing a way to quantify the resulting uncertainties.

Contribution

It introduces a method to quantify the amplification of errors caused by modeling inaccuracies in the equilibrium function of the linearized BGK equation.

Findings

Error amplification depends on perturbations in velocity and temperature

Quantitative bounds on solution errors are derived

Analysis aids in understanding robustness of kinetic models

Abstract

We consider the linearized BGK equation and want to quantify uncertainties in the case of modelling errors. More specifically, we want to quantify the error produced if the pre-determined equilibrium function is chosen inaccurately. In this paper we consider perturbations in the velocity and in the temperature of the equilibrium function and consider how much the error is amplified in the solution.