A Novel Construction of Distribution Function through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy

In this paper, we propose a new way to construct the distribution function through 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 Hermite polynomial expansion which yields Grad's 13-moment distribution function; Second, all moments of the present distribution function are determined from conservation laws; Third, these moments are closely linked to the most desirable variables, such as mass, momentum and energy. Then, this new distribution function is applied to construct a new gas kinetic flux solver. Numerical validations show that the proposed method 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.