Comparison of shock wave structures by solving Burnett and Boltzmann equations

Abstract

Two new computer codes have been developed to solve the one-dimensional Burnett equations and the Boltzmann-BGK equation for the prediction of shock structure. For the Burnett equations, the numerical technique is based on a four-stage Runge-Kutta timeintegrating method. Second-order upwind flux differencing with Roe’s nonlinear flux limiter was adopted to discretize the convective terms. The Burnett stress and heat flux t e r m are discretized using central differencing and are treated explicitly as source terms. For the Boltzmann-BGK equation, the distribution function, f ( t , r , ( 1 , & ! , ( 3 ) , is transformed into two partial differential equations by integrating it with respect to molecular velocity space ((r,(s). These two equations are ithen solved using the same four-stage Runge-Kutta time integration method coupled with the Discrete-Ordinate method (DOM). Shock wave structures have been studied. Results are compared with available experimental data. It was found that the Burnett equations predict very accurate shock wave structure compared to Boltzmann and experimental data.