Abstract
In this paper, the BGK (Bhatnagar-Gross-Krook) 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 MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws)-type initial reconstruction. While, an implicit-type time integration method known as the AF-ADI (Approximate Factorization - Alternating Direction Implicit) is adopted for computing both steady and unsteady computations. Two typical hypersonic flow problems are selected in this study in order to test the gas-kinetic scheme's characteristics and performance, namely, the blunt body, and the double Mach reflection problems. The numerical findings of the BGK scheme via these tests indicate that this technique is robust, accurate and stable for hypersonic flow.
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