The impacts of time-step size in the application of the direct simulation Monte Carlo method to ultra-thin gas film lubrication

Abstract

The size of the time step is an important factor in the application of the direct simulation Monte Carlo (DSMC) method for rarefied gas dynamics. In order to understand the effects of this essential factor and then to apply the DSMC method more effectively, the influence of the size of time step used on the accuracy of the algorithm is demonstrated and investigated. It is found that some wall properties related to the streamwise derivative of velocity, such as wall shear stress, are sensitive to the size of time step. A series of computation and analysis is presented to illustrate the computational errors (bias) caused by the size of time step and the corresponding computational resource applied. From this investigation, a compromise can be made between the magnitude of error and computing cost; thus, a criterion on the size of time step is proposed for the DSMC method. This criterion is necessary for the application of the DSMC method used in a low subsonic, ultra-thin gas film lubrication with a characteristic scale of one mean free path, such as the gas bearing flow under the floating slider.