Numerical Solution of the Taylor-Quette Flow Problem: A Commodious Statistical Approach

Problem statement: The main problem in solving of the Boltzmann equation by statistical methods is its long computational time (CPU time). The problem of decreasing of CPU time usage in statistical solution methods of Boltzmann equation for rarefied vortex flows was studied. Approach: In this study the Boltzmann equation in a rarefied Taylor-Quette flow regime was solved using the new Monte Carlo method which is officially named time Relaxated Mont Carlo method that applied the equilibrium conditions in each time step. Results: The results obtained from time Relaxated Mont Carlo method for the problem at hand were compared with those from the usual Direct Simulation Monte Carlo method. This comparison showed good agreement between the two sets of results. Conclusion: Whereas, the number of collisions and CPU usage time in the suggested method, as compared to the direct simulation Monte Carlo method, showed a significant decrease.