Switching criteria for hybrid rarefied gas flow solvers

Abstract

Switching criteria for hybrid hydrodynamic/molecular gas flow solvers are developed, and are demonstrated to be more appropriate than conventional criteria for identifying thermodynamic non-equilibrium. For switching from a molecular/kinetic solver to a hydrodynamic (continuum-fluid) solver, the criterion is based on the difference between the hydrodynamic near-equilibrium fluxes (i.e. the Navier-Stokes stress and Fourier heat flux) and the actual values of stress and heat flux as computed from the molecular solver. For switching from hydrodynamics to molecular/kinetic, a similar criterion is used but the values of stress and heat flux are approximated through higher order constitutive relations; in this case, we use the R13 equations. The efficacy of our proposed switching criteria is tested within an illustrative hybrid kinetic/Navier-Stokes solver. For the test cases investigated, the results from the hybrid procedure compare very well with the full kinetic solution, and are obtained at a fraction of the computational cost.

A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas

“…The assumption that microscopic relaxation processes are not of concern is, however, inadequate in flows where the microscopic relaxation time is comparable to the characteristic time of evolution of the macroscopic field variables. In the kinetic theory of dilute gases, such flows are identified with high Knudsen numbers (conventionally defined as a ratio of the average time between molecule/molecule collisions to a macroscopic characteristic time of the flow, however see [2]). Experimental observations of sound wave propagation at high Knudsen number challenge many continuum hydrodynamics and kinetic theory models [3,4,5,6]; it is well-known that the Navier-Stokes-Fourier model fails to predict sound wave propagation at high Knudsen number.…”

Multiscale lattice Boltzmann approach to modeling gas flows

“…However, different parameters may give significantly different values. So defining an appropriate switching criterion remains an interesting problem in itself [2,13]. Here, we do not intend to investigate the switching criterion and will use what has been reported in the literature.…”

Breakdown parameter for kinetic modeling of multiscale gas flows

“…A similar approach has been used in Ref. [2] to obtain breakdown parameters based on macroscopic flow properties. We call this approach here the "NSF breakdown indicator," and it could provide a better way of assessing the NSF equations indirectly.…”

“…Multiscale methods are needed when gas flows have a broad range of rarefaction levels (see, for example, Refs. [2][3][4][5][6][7][8][9][10][11][12][13][14][15], and references therein). The conventional Navier-Stokes-Fourier (NSF) equations are computationally efficient but are only valid in the hydrodynamic regime.…”

“…The global Knudsen number has often been used [2]. Other parameters are also suggested, such as Tsien's parameter [23], Bird's parameter P [24], the local Knudsen number [13,14], Tiwari's criterion [25], the parameter B [26], the criterion proposed by Lockerby et al [2], and some others [27,28]. Although these breakdown parameters have had some success, in particular, for high-speed flows, it is fair to say that there is no general parameter available.…”