The development and application of the moment method in the gas kinetic theory

Abstract

The moment method is not only a modeling tool that gives macroscopic fluid equations by reducing kinetic equations, but also a numerical method for solving kinetic equations. It has been the subject of rapid development, and in recent years has acquired widespread applications. In this paper, we review and summarize the research development of moment methods in kinetic theory from the aspects of modeling, numerical methods, and applications. First, we discuss the deficiencies of moment methods and summarize the remedy, where in particular the regularized moment method and globally hyperbolic moment method are introduced, owing to the wide interest regarding them. Subsequently, we investigate various numerical methods for solving moment equations, and highlight the numerical regularized method for moment equations of arbitrary orders. In addition, this paper reviews the applications of moment methods in the fields of rarefied gases, microflows, electron transport, plasma, and density functionals and presents an outlook regarding the future development of moment methods.