“…Huang et al [5] used flow-adapted discrete velocities, a non-unique equilibrium distribution constrained by a set of linear moments and used interpolated nodes. Prendergast and Xu [6], Kim et al [7] and Koltelnikov and Montgomery used Bhatnagar-Gross-Krook type model [8] to establish new type flux and employed TVD flux limitation with the neighborhood cells, Rena et al [9], Vahala et al [10] , Qian [11,12],Sun [13], De Cicco et al [14], Mason [15,16], Yan [17,18], and Kataoka and Tsutahara [19,20] proposed many models by using additional techniques to achieve higher Mach number for the compressible flows [21]. Among the existing models for the compressible flows, the one by Kataoka and Tsutahara (KT) has a simple and rigorous theoretical background [22].…”