Hypersonic flow simulation by the gas-kinetic bhatnagar-gross-krook scheme - Chit, O.J.; Omar, Ashraf Ali; Asrar, Waqar; Zaludin, Z. A. (The American Institute of Aeronautics and Astronautics (AIAA), 2005)
The gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme is extended to hypersonic ﬂow simulations and thus shows that the compressible inviscid ﬂow solutions of the simulations are efﬁciently and accurately obtained from the BGK scheme without the disastrous shock instability phenomenon that occurs in most hypersonic ﬂow simulations involving strong shock waves. For this particular study, the effect of chemistry in hypersonic ﬂows has not been taken into account. Hence, the assumption of calorically perfect gas is imposed in all simulations. The high-order resolution of the scheme is achieved by utilizing monotone upstream-centered schemes for conservation laws-type initial reconstruction. While, an implicit-type time-integration method known as the approximate factorization– alternating direction implicit is adopted for computing both steady and unsteady calculations. The gas-kinetic scheme is tested meticulously in four two-dimensional numerical examples, namely, the blunt-body problem, the double Mach reﬂection problem, the axisymmetric blunt-body problem, and the ﬂow over a 15-deg ramp. The numerical results of the BGK scheme when compared with the other schemes and experimental data show that this numerical technique is robust, accurate, and stable for hypersonic ﬂow.