NUMERICAL INVESTIGATION OF THE BOLTZMANN EQUATION BY TRMCMETHOD TO SIMULATE FLOW OVER A FLAT NANOPLATE

In the present study, first, second and third orders of the TRMC scheme, called TRMC1, TRMC2 and TRMC3, are employed to numerically investigate the flow over a nano-plate. 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 is observed that the results obtained from the TRMC3 method have excellent agreement with those of the DSMC method. On the other hand the results obtained from TRMC1 and TRMC2 methods show deviation compared to the DSMC method. The deviations are more pronounced for the temperature and pressure distributions. It is 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 flow over the nano-plate with reasonable time step and appropriate complexity.

Keywords:

Boltzmann equation , direct simulation Monte Carlo method , time relaxed Monte Carlo method , higher order collision , nano-plate