NUMERICAL INVESTIGATION OF THE BOLTZMANN EQUATION BY TRMC METHOD TO SIMULATE LID DRIVEN MICRO CAVITY PROBLEM

Recently Time relaxed Monte Carlo method, TRMC, has been introduced as a simple and efficient method for numerical solution of the Boltzmann equation. In the current study, first, second and third orders of TRMC scheme, called TRMC1, TRMC2 and TRMC3, are employed to numerically investigate the lid driven micro cavity flow. Higher order terms in the Wild sum expansion have been considered to obtain higher order collisions. The results are compared with those from the DSMC method. It was observed that the results obtained from the TRMC3 method have excellent agreement with those of the DSMC method. On the other hand the results of TRMC1 and TRMC2 methods show deviation compared to the DSMC method. The deviations are more pronounced for the velocity distributions. It was concluded that the Maxwellian truncation of the Wild sum expansion to obtain TRMC3 scheme may be a proper alternative for the DSMC method in simulating the lid driven micro cavity problem with reasonable time step and appropriate complexity.

Keywords:

Boltzmann equation , direct simulation Monte Carlo , time relaxed Monte Carlo , higher order collision , micro cavity