Complete third-order polynomial expansion-based gas kinetic flux solver for flows from continuum regime to rarefied regime

Abstract

The Grad's 13 distribution function was derived through a third-order Hermite polynomial expansion in terms of peculiar velocity. Recently, it has been adopted to construct a gas kinetic flux solver called G13-GKFS for simulation of flows from the continuum regime to the rarefied regime. However, this Grad's distribution function only considers the contracted polynomials that strictly satisfy orthogonality. In other words, the third-order terms of CiC12, CiC22, and CiC32 share the same coefficients (γi). However, the results from the discrete velocity method reveal that those coefficients could be different, especially in the rarefied regime. This may affect the accuracy of numerical results in the rarefied region. In order to consider different coefficients of the third-order terms, we propose a complete third-order polynomial expansion to approximate the distribution function in this work. To show the capability of current distribution function, a new GKFS is developed for flows from the continuum regime to the rarefied regime. Some benchmark cases are solved to demonstrate that the new GKFS outperforms the G13-GKFS in the rarefied regime.