On the time relaxed Monte Carlo computations for the lid-driven micro cavity flow

In the present study, the first, second and third orders of the TRMC scheme (TRMC1, TRMC2 and TRMC3 schemes) are employed to numerically investigate the lid-driven micro cavity flow with different lid velocities and Knudsen numbers. The simulations cover flow regimes from early slip to early transition regimes (0.005≤Kn≤0.1). Higher order terms in the Wild sum expansion are considered to obtain higher order collisions. The results are compared with those from the standard DSMC method. Comparisons show that among the studied schemes, the results obtained from the TRMC3 scheme have excellent agreement with the ones from the DSMC method. On the other hand, the results of TRMC1 and TRMC2 schemes show deviations compared to those from the DSMC method. The deviations are more pronounced for the velocity distributions. Moreover, the present investigation illustrates that as the Knudsen number increases the accuracy of lower orders of the TRMC scheme improves. It is observed that truncating the Wild sum expansion up to the third order approximation of the TRMC scheme, may be a proper alternative method for the DSMC method in simulating the lid-driven micro cavity problem for Knudsen numbers 0.005≤Kn≤0.1 with reasonable accuracy and simplicity in mathematics.