Discrete Boltzmann trans-scale modeling of high-speed compressible flows

摘要

We present a general framework for constructing trans-scale discreteBoltzmann models (DBMs) for high-speed compressible flows ranging fromcontinuum to transition regime. This is achieved by designing a higher-orderdiscrete equilibrium distribution function which satisfies additionalnonhydrodynamic kinetic moments. In order to characterize the thermodynamicnonequilibrium effects (TNE) and estimate the condition under which the DBMs atvarious levles should be used, two novel measures are presented: (i) therelative TNE strength, describing the relative strength of the (N + 1)-th orderTNE to the N-th order one; (ii) the TNE discrepancy between DBM simulation andrelevant theoretical analysis. Whether or not the higher-order TNE should betaken into account in the modeling and which level of DBM should be adopted, isbest described by the relative TNE intensity and/or discrepancy rather than bythe value of the Knudsen number. As a model example, a two-dimensional DBM with26 discrete velocities at Burnett level is formulated, verified and validated.