A comparative study of discrete velocity methods for low-speed rarefied gas flows. (15th January 2018)

• Record Type: Journal Article
• Authors: Wang, Peng; Ho, Minh Tuan; Wu, Lei; Guo, Zhaoli; Zhang, Yonghao
• Is Part Of: Computers & fluids. Volume 161(2018)
• Page Start: 33
• Page End: 46
• Publication Date: 2018-01-15
• Subjects: Gas kinetic equation -- Rarefied flow -- Discrete velocity method -- Discrete unified gas kinetic scheme; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2017.11.006
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Accuracy and computational efficiency of the two DVM methods are studied. In the near hydrodynamic flow regime, DUGKS seems to have advantages. For rarefied steady flows, the implicit GDVM may be preferred. Abstract: In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. Although various versions of DVM have been developed, their performance, in terms of modeling accuracy and computational efficiency, is yet to be comprehensively studied in all the flow regimes. Here, the traditional third-order time-implicit Godunov DVM (GDVM) and the recently developed discrete unified gas-kinetic scheme (DUGKS) are analysed in finding steady-state solutions of the low-speed force-driven Poiseuille and lid-driven cavity flows. With the molecular collision and free streaming being treated simultaneously, the DUGKS preserves the second-order accuracy in the spatial and temporal discretizations in all flow regimes. Towards the hydrodynamic flow regime, not only is the DUGKS faster than the GDVM when using the same spatial mesh, but also requires less spatial resolution than that of the GDVM to achieve the same numerical accuracy. From the slip to free molecular flow regimes, however, the DUGKS is slower than the GDVM, due to the complicated flux evaluation and the restrictive time step which is smaller than the maximum effective time step of the GDVM. Therefore, the DUGKS is preferable for problems involving different flow regimes, particularly when the hydrodynamic flow regime is dominant. For highly rarefied gas flows, if the steady-state solution is mainly concerned, the implicit GDVM, which can boost the convergence significantly, is a better choice.