A novel gas kinetic flux solver for simulation of continuum and slip flows. (14th June 2021)

• Record Type: Journal Article
• Authors: Yuan, Zhenyu; Yang, Liming; Shu, Chang; Liu, Zijian; Liu, Wei
• Is Part Of: International journal for numerical methods in fluids. Volume 93:Number 9(2021)
• Page Start: 2863
• Page End: 2888
• Publication Date: 2021-06-14
• Subjects: gas kinetic flux solver -- macroscopic variables -- numerical quadrature -- spatial derivatives; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.5013
• Languages: English
• ISSNs: 0271-2091

Abstract

Abstract: In this work, a novel gas kinetic flux solver (GKFS) is presented for simulation of compressible and incompressible flows in the continuum and slip regimes. The finite volume method is adopted to discretize the governing differential equations, and inviscid and viscous fluxes at the cell interface are evaluated simultaneously by the local solution to the Boltzmann equation. Different from the conventional GKFS, in which the local solution to the Boltzmann equation is divided into the equilibrium part and the nonequilibrium part and the nonequilibrium distribution function is approximated by the difference of equilibrium distribution functions at the cell interface and its surrounding points, the present solver evaluates the local solution by integrating the Boltzmann equation along the characteristic line. As a result, the local solution to the Boltzmann equation consists of the equilibrium distribution function at the cell interface and the initial distribution function at the surrounding points. In the present work, the initial distribution function is given from the first‐order Chapman–Enskog expansion. Finally, the distribution function at the cell interface is only relevant to the macroscopic variables and their spatial derivatives. Accordingly, the fluxes across the cell interface can be evaluated by the moments of the distribution function at the cell interface. Test results show that the present solver can provide accurate numerical predictions for flows in both continuum and slip regimes. Abstract : In this study, a novel gas kinetic flux solver (GKFS) is proposed for simulation of flows in continuum and slip regimes. The initial gas distribution function around the cell interface for present solver is expressed explicitly as the function of conservative variables and their derivatives. Hence, the numerical approximation of nonequilibrium distribution function in the conventional GKFS can be removed effectively. Numerical experiments show that both compressible and incompressible viscous flows can be well simulated by the developed novel GKFS.