A new approach to calculate the axially symmetric binary gas flow is proposed. Dalton's law for partial pressures contributed by each species of a binary gas mixture (argon and helium) is incorporated into numerical simulation of rarefied axially symmetric flow inside a rotating cylinder by using the time relaxed Monte-Carlo (TRMC) scheme and the direct simulation Monte-Carlo (DSMC) method. The results of flow simulations are compared with the analytical solution and results obtained by Bird [1]. The results of the flow simulations show better agreement than the results obtained by Bird [1] in comparison with the analytical solutions. However, the results of the flow simulations using the TRMC scheme show better agreement than those obtained using the DSMC method in comparison with the analytical solutions.
A new algorithm for the simulation of the boltzmann equation using the direct simulation monte-carlo method † Abstract A new algorithm, the modified direct simulation Monte-Carlo (MDSMC) method, for the simulation of CouetteTaylor gas flow problem is developed. The Taylor series expansion is used to obtain the modified equation of the firstorder time discretization of the collision equation and the new algorithm, MDSMC, is implemented to simulate the collision equation in the Boltzmann equation. In the new algorithm (MDSMC) there exists a new extra term which takes in to account the effect of the second order collision. This new extra term has the effect of enhancing the appearance of the first Taylor instabilities of vortices streamlines. In the new algorithm (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 algorithm. The appearance of the first Taylor instabilities of vortices streamlines using the MDSMC algorithm at different ratios of ω ν (experimental data of Taylor [1]) occurred at less time-step than using the DSMC algorithm. The results of the torque developed on the stationary cylinder using the MDSMC algorithm show better agreement in comparison with the experimental data of Kuhlthau [2] than the results of the torque developed on the stationary cylinder using the DSMC algorithm.
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.
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