DSMC simulation of micro/nano flows using SBT-TAS technique

Abstract

The aim of the current paper is to decrease the required computational time and memory of the direct simulation Monte Carlo (DSMC) method using the simplified Bernoulli-trials (SBT) collision algorithm in combination with the transient adaptive subcell (TAS) technique. It is already shown that SBT collision could provide accurate solutions with a few particles per cell, when the requirement for grid resolution of the pure SBT remains the same as standard DSMC collision algorithms. Here, we demonstrate that the combination of the SBT with the TAS technique could reduce the number of required cells considerably, especially for low Kn micro/nano flows, while the accuracy is preserved and computational time decreases. The efficiency of the SBT-TAS is investigated for two typical test cases, i.e., low Knudsen/low speed flow in micro cavity and high speed/high gradient flow over the nano-scale flat plate. We tested cavity flow at Kn=0.005 and show that SBT-TAS solution using a coarse grid of 50×50 agrees suitably with the NTC solution using a 200×200 cell with 2×2 fixed subcells and number of particles per cell PPC=20 (called correct solution), see Fig. 4, while the computational time of the SBT-TAS decreases by 64%. We show that using of TAS grid movement (SBT-TAS-Dual) decreases the mean collision separation; however, accuracy gain is almost slight compared to the extra computational cost of the grid movement. We will show that product of the local Knudsen number by the average subcells number in a cell is constant. For flow over the flat plate geometry, we will show that even though TAS scheme could provide enough number of collision subcells even for quite coarse grids, the smearing of gradients due to larger sample cell size could deteriorate the final solution.