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The BGK model of the Boltzmann equation allows for efficient flowsimulations, especially in the transition regime between continuum and highrarefaction. However, ensuring efficient performances for multiscale flows, inwhich the Knudsen number varies by several orders of magnitude, is neverstraightforward. Discrete velocity methods as well as particle-based solverscan each reveal advantageous in different conditions, but not withoutcompromises in specific regimes. This article presents a second-orderasymptotic preserving discrete velocity method to solve the BGK equation, withthe particularity of thoroughly maintaining positivity when operations areconducted on the distribution function. With this procedure based onexponential differencing, it is therefore also possible to construct an adaptedversion of this second-order method using the stochastic particle approach, aspreviously presented. The deterministic variant is detailed here and itsperformances are evaluated on several test cases. Combined to the probabilisticsolver and with the possibility of a future coupling, our exponentialdifferencing DVM provides a robust toolbox that would be useful in efficientlysimulating multiscale gas phenomena.

An Asymptotic Preserving Discrete Velocity Method based on Exponential Bhatnagar-Gross-Krook Integration