TY - JOUR
T1 - A Novel Construction of Distribution Function Through Second-Order Polynomial Approximation in Terms of Particle Mass, Momentum and Energy
AU - Yuan , Z. Y.
AU - Chen , Z.
AU - Shu , C.
AU - Liu , Y. Y.
AU - Zhang , Z. L.
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 738
EP - 770
PY - 2024
DA - 2024/02
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2023-0107
UR - https://global-sci.org/intro/article_detail/aamm/22936.html
KW - Second-order truncated expansion, peculiar velocity space, compatibility conditions and moment relationships, gas kinetic flux solver, continuum regime to rarefied regime.
AB - <p style="text-align: justify;">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.</p>