A simplified discrete unified gas–kinetic scheme for compressible flow

Abstract

In this paper, the simplified discrete unified gas-kinetic scheme presented in the former paper is extended from incompressible flow to compressible flow at a high Mach number. In our earlier work, a simplified discrete unified gas–kinetic scheme was developed for low-speed flow in which the Mach number is small for keeping the incompressible property. To simulate compressible flow, the governing equation of the internal energy distribution function presented as potential energy including the Prandtl number effect is introduced to the present method. The velocity field is coupled with density and internal energy by the evolution of distribution functions related to mass, momentum, and temperature. For simplification and computational efficiency, the D2Q13 circular distribution function is applied as the equilibrium model. Compared to our earlier work, higher Mach number flows can be simulated by the proposed method, which is of the ability to simulate compressible flow. A number of numerical test cases from incompressible to compressible flows have been conducted, including incompressible lid-driven cavity flow, Taylor vortex flow, transonic flow past NACA (National Advisory Committee for Aeronautics) 0012 airfoil, Sod shock tube, supersonic flow past a circular cylinder, and isentropic vortex convection. All simulation results agree well with the reference data.

Free-Energy-Based Discrete Unified Gas Kinetic Scheme for van der Waals Fluid

“…With the information of the Knudsen number incorporated in the construction of the interface flux, the DUGKS exhibits the capability of properly modeling a wide range of fluid flows ranging from the continuum regime to the free-molecule regime [ 32 ]. Over the past decade, the DUGKS has proven its excellent performance in predicting microscale gas flows [ 33 , 34 ], multicomponent gas flows [ 35 , 36 ], turbulent flows [ 37 , 38 , 39 ], compressible flows [ 40 , 41 , 42 ], radiative heat transfer [ 43 , 44 ], and so forth [ 45 ]. A comparative study [ 46 ] has demonstrated the stability superiority of the DUGKS over that of the LB method in terms of nearly incompressible flows.…”

Pseudopotential-based discrete unified gas kinetic scheme for modeling multiphase fluid flows

“…By considering the local Knudsen information in the construction of kinetic flux, DUGKS could accurately depict extensive fluid flows ranging from the continuum regime to the free molecular regime [28]. Over the past decade, DUGKS has demonstrated its excellent capability in modeling compressible flows [29][30][31], turbulent flows [32][33][34], solid-fluid flows [35][36][37], multicomponent gas flows [38,39], microscale gas flows [40,41], radiative heat transfer [42,43], and so forth. For the widespread application of DUGKS, readers are recommended to refer to the review literature provided by Guo and Xu [44].…”

Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical-systems

“…Furthermore, as the DUGKS is an unsteady flow simulation method in nature, the ensemble averages are not required compared with the DSMC method. Currently, some improved and enhanced schemes based on the DUGKS also have been developed [25,26,27]. And, Wang et al [28] proposed an arbitrary Lagrangian-Eulerian-type DUGKS for solving the moving boundary problems in continuum and rarefied gas flows.…”