A Novel Construction of Distribution Function Through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, we propose a new way to construct the distribution functionthrough the second-order polynomial approximation in terms of particle mass, momentum and energy. The new construction holds three distinguished features. First,the formulations are more concise as compared with the third-order truncated Hermitepolynomial expansion which yields Grad’s 13-moment distribution function; Second,all moments of the present distribution function are determined from conservationlaws; Third, these moments are closely linked to the most desirable variables, suchas mass, momentum and energy. Then, this new distribution function is applied toconstruct a new gas kinetic flux solver. Numerical validations show that the proposedmethod recovers the Navier-Stokes solutions in the continuum regime. In addition,it outperforms Grad’s 13-moment distribution function in the transition regime, especially in the prediction of temperature and heat flux.