Numerical modeling of the gas flow past a flat plate over a wide range of gas rarefaction and Mach number in the framework of a kinetic model for the Boltzmann equation

Abstract

The aim of the present work is the numerical modeling of the gas flow past a flat plate at zero angle of attack with basis in the kinetic model proposed by Bhatnagar, Gross and Krook for the non-linear Boltzmann equation. The influence of the gas-surface interaction law on the solution of the problem will be analyzed by using the diffuse scattering kernel proposed by Maxwell as well as the kernel proposed by Cercignani and Lampis which allows the setting of two accommodation coefficients of gas molecules at the surface, namely the tangential momentum and normal energy accommodation coefficients. The Discrete Velocity Method will be employed to solve the problem. To overcome the numerical problem of discontinuity of the distribution function of molecular velocities near the leading and trailing edges of the plate, a numerical technique proposed by Prof. Irina Graur and coworkers, which is based on the Total Variation Diminishing method for approximating the spatial derivatives, will be implemented in the numerical scheme. The approach also has the advantage of allowing to solve the problem in case of non-steady state and then obtain the steady state solution as a limiting case. As results, the drag coefficient on the plate and the flow fields around it will be calculated over a wide range of the Knudsen number and Mach number. Some results will be compared to data available in the literature. The comparison with data obtained from the direct simulation Monte Carlo method allows to verify the range of Mach number in which the Monte Carlo method can be used (usually the Monte Carlo method is used for supersonic and hypersonic flows). Moreover, the setting of some pairs of accommodation coefficients will allow to analyze the influence of the gas-surface interaction on the solution of the problem and discuss the peculiarities inherent to the rarefied gas flow.