The accuracy of the gas-kinetic BGK finite difference method for solving 3-D compressible inviscid flows - Ong, Jiunn Chit; Omar, Ashraf Ali; Asrar, Waqar (2011)
In this paper, the descriptions on the development of a flow solver for the threedimensional compressible Euler equations are presented. The underlying numerical scheme for the solver was based on the collisional Boltzmann model that produces the gas-kinetic BGK (Bhatnagaar-Gross-Krook) scheme. In constructing the desired algorithm, the convection flux terms were discretized by a semi-discrete finite difference method. The resulting inviscid flux functions were approximated by the gas-kinetic BGK scheme. To achieve higher order spatial accuracy, the cell interface primitive flow variables were reconstructed via the MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) interpolation method coupled with a min-mod limiter. As for advancing the solutions to another time level, an explicit-type time integration method known as the modified fourth-order Runge-Kutta was employed in the current flow solver to compute steady-state solutions. Two numerical cases were used to validate the flow solver where the computed results obtained were compared with available analytical solutions and published results from literature to substantiate the accuracy and robustness of the developed gas-kinetic BGK flow solver.