Computational Analysis of Gas Kinetic Bhatnagar-Grosskrook Scheme for Inviscid Compressible Flow

Many numerical schemes have been developed in the field of computational fluid dynamics to simulate inviscid, compressible flows.Among those most notable and successful are the Godunov-type schemes and flux vector splitting schemes.Besides these numerical schemes, schemes based on the gas kinetic theory have been developed in the past few years.Stemming from this approach, the gas kinetic Bhatnagar-Gross-Krook (BGK) scheme is realized.In this thesis, the BGK scheme based on the BGK model of the approximate Boltzmann equation has been fully analyzed and developed accordingly.The numerical algorithms for the BGK scheme are first developed for simulating one-dimensional flow, and then follow by the-two dimensional flow realms. Higher-order spatial accuracy of the scheme is achieved through the reconstruction of the flow variables via the Monotone Upstream-Centered Schemes for Conservation Laws (MUSCL) approach. For time integration method, an explicit method is adopted for the first-order schemes in both one and two-dimensional flow problems.The classical Runge-kutta multistage method is employed only for schemes with higher-order of accuracy. In addition, an implicit time integration method known as the Approximate Factorization-Alternating Direction Implicit (AF-ADI) would be employed when dealing with two-dimensional flow problems in higher-order.In order to investigate the computational characteristics of the BGK scheme in detail, several cases of shock-shock interaction problem have been numerically analyzed.Developed code for the onedimensional flow is validated with three typical test cases, namely,quasi-onedimensional supersonic-subsonic nozzle flow, shock tube, and two interacting blast waves.Likewise,four typical two-dimensional test cases that are found in the literatures are used to validate the developed code for the two-dimensional flow.They are regular shock reflection,supersonic flow over a wedge, channel with a fifteen-degree ramp, and flow past a cylinder.From these validation cases, computed results are compared with the available exact solutions and with other computational results obtained by using some well known numerical discretization schemes.In comparison,the BGK scheme exhibits the most accurate shock resolution capabilities,least diffusiveness, least oscillatory,and great robustness.

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