Comparative study between finite difference and finite volume methods for gas-kinetic BGK scheme / Ong Jiunn Chit, Lim Jiunn Hsuh and Muhamad Othman

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 haven been developed in the past few years. Stemming from this approach, the gas kinetic Bhatnagar-Gross-Krook (BGK) scheme is realized. In this research, the BGK scheme based on the BGK model of the approximate Boltzmann equation has been fully analyzed and developed accordingly. The BGK scheme is formulated based on a semi-discrete finite volume framework. 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, the classical Runge-Kutta multi-stage method is employed. In order to fully understand the computational characteristics of the BGK scheme, three test cases are selected to assess the numerical scheme. Then, the semi-discrete finite volume BGK scheme's results are compared against the second-order central difference scheme with Total Variation Diminishing (TVD) using a finite difference approach. In comparison, the BGK scheme exhibits the most accurate shock resolution capabilities, least diffusiveness, least oscillatory and great robustness.