Implementation of asymptotic preserving discrete velocity methods into the simulation code PICLas

The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction . However, ensuring efficient performances for multiscale flows, in which the Knudsen number varies by several orders of magnitude, is never straightforward. Discrete velocity methods as well as particle-based solvers can each reveal advantageous in different conditions, but not without compromises in specific regimes. This article presents a second-order asymptotic preserving discrete velocity method to solve the BGK equation, with the particularity of maintaining positivity when operations are conducted with the cell-local distribution function. With this procedure based on exponential differencing, it is therefore also possible to construct an adapted version of this second-order method using the stochastic particle approach, as presented in Pfeiffer et al. [1] . The deterministic variant and its implementation are detailed here and its performances are evaluated on several test cases. Combined to the probabilistic solver and with the possibility of a future coupling, our exponential differencing discrete velocity method provides a robust toolbox, useful for efficiently simulating multiscale gas phenomena.