A new scheme developed for the numerical simulation of the Boltzmann equation using the direct simulation monte-carlo scheme for the flow about a sphere

Abstract

A new scheme, the modified direct simulation Monte-Carlo (MDSMC), for the numerical simulation of the Boltzmann equation for rarefied gas flow about a sphere is developed. The Taylor series expansion is used to obtain the modified equation of the first-order time discretization of the collision equation and the new scheme, MDSMC, is implemented to simulate the collision equation in the Boltzmann equation. In the new scheme (MDSMC) there exists a new extra term which takes into account the effect of the second-order collision. In the new scheme (MDSMC) there also exists a second-order term in time step in the probabilistic coefficients which has the effect of simulation with higher accuracy than the previous DSMC scheme. The results of the drag coefficient of the sphere using the MDSMC scheme show better agreement in comparison with the experimental data of Wegener (1961) than the results of the drag coefficient of the sphere using the DSMC scheme.